ANL-6335 Chemist ry ( T I D - 4 5 0 0 , 16th Ed.)

AEC R e s e a r c h and Development Report

ARGONNE NATIONAL LABORATORY 9700 South Cass Avenue

ArgonnCs Illinois

A STUDY OF THE EMANATION METHOD FOR THE DETERMINATION OF THE SURFACE AREA OF THORIUM OXIDE

by

S. B. Skladzien

Reactor Engineering Division

Apr i l 1961

Operated by The Univers i ty of Chicago under

Contract W-31-109-eng-38

DISCLAIMER

This report was prepared as an account of work sponsored by an agency of the United States Government. Neither the United States Government nor any agency Thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

DISCLAIMER Portions of this document may be illegible in electronic image products. Images are produced from the best available original document.

TABLE OF CONTENTS

Page

ABSTRACT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5

2. SAMPLE PREPARATION . . . . . . . . . . . . . . . . . . . . . . . . . . 7

3. PROPORTIONAL COUNTER . . . . . . . . . . . . . . . . . . . . . . . . 7

4. OPERATING CHARACTERISTICS OF THE SYSTEM . . . . . . . . 10

5. THEORY OF THE EMANATION PROCESS . . . . . . . . . . . . . . . 12

6. RECOIL RANGE OF R n " ° . . . . . . . . . . . . . . . . . . . . . . . . . . 15

7. DETERMINATION OF RECOIL EMANATION BY a COUNTING . 16

8. EMANATION MEASUREMENTS . . . . . . . . . . . . . . . . . . . . . . 17

9. SUMMARY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

APPENDICES

A. The BET Low- t empera tu re Absorpt ion Method for Determining Surface A r e a s . . . . . . . . . . . . . . . . . . . . . . . 26

B. Derivat ion of the Express ion for E|^ . . . . . . . . . . . . . . . . 27

C. Calculation of Recoil Range of Rn^^ . . . . . . . . . . . . . . . . . 29

D. Background Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

BIBLIOGRAPHY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

LIST OF TABLES

No. Title Page

1 Change in E;^ and Surface Area a s a Function of F i r ing Tempera tu re . . . . . . . . . . . . . . . . . . . . . . . . . . . 18

2 Change in Eg_ and Surface Area as a Function of Fi r ing Time at 500°C . . . . . . . . . . . . . . . . . . . . . . . . . . 20

3 Change in ER_ and Surface Area as a Function of F i r ing Time at 900°C . . . . . . . . . . . . . . . . . . . . . . . . . . 21

4 Change in ER_ and Surface Area of ThOg-UOz - ^ Function of Fir ing Tempera tu re . . . . . . . . . . . . . . . . . . . 22

5 Net Counting Rate after Correc t ing for Deposited Background. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

LIST OF FIGURES

No. Title Page

1 Spher ical P a r t i c l e s of Thor ium Oxide-Uranium Oxide

F i r e d for 1 Hr at 650°C. . . . . . . . . . . . . . . . . . . . . . . . . 8

2 Cyl indrical Geometry Propor t iona l Spect rometer . . . . . . . 9

3 Block Diagram of Elec t ronic Circuit , Counter, and

Sampling System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

4 Thoron Decay Scheme and Alpha Ene rg i e s . . . . . . . . . . . . 10

5 Typical Emanat ion Spectrum from Thorium Oxide . . . . . . . 10

6 Count Rate as a Function of Gas Flow . . . . . . . . . . . . . . . 12

7 Thor ium or 4n Ser ies . . . . . . . . . . . . . . . . . . . . . . . . . . 14

8 Thoron Activity at Time t after Thor ium Separa t ion . . . . . . 15

9 Alpha Spectrum of Deposited Background Activity . . . . . . . 17 10 Change of Recoil Emanat ion from Thorium Oxide a s a

Function of Fir ing Tempera tu re . . . . . . . . . . . . . . . . . . . 19

11 Change in Density as a Function of Fi r ing Tempera tu re . . . 19

12 Surface Area Change a s a Function of Fir ing Tempera tu re . 19

13 Change in Surface Area as a Function of Fi r ing Time at 500°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

14 Change in Surface Area as a Function of Fir ing Time at 900°C . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

15 Surface Area Change as a Function of Fi r ing Tempera tu re

for ThOa-UOa System . . . . . . . . . . . . . . . . . . . . . . . . . . 23

16 Recoil from a Spher ical Surface where r » R . . . . . . . . . . 27

17 Correc t ion for Var iable Background Activity Deposited in Counter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30

A STUDY OF THE EMANATION METHOD FOR THE DETERMINATION OF THE SURFACE AREA OF THORIUM OXIDE

by

S. B. Skladzien

ABSTRACT

The surface a r e a s of severa l thorium oxide and tho­r ium oxide-uranium oxide p repa ra t ions were m e a s u r e d by the emanation method. The radioact ive gas-counting sys tem employed is descr ibed , and a discussion of the procedure for converting counting data to t e r m s of emanating power and finally to surface a r e a values is given. Surface a r e a values by the emanat ion method a re compared with BET values from like samples . The difference between values obtained by the two methods is a t t r ibuted to the efficiency of the radioact ive gas-de tec t ing sys tem and the porosi ty of the oxide samples . The contribution of Rn^^^ from the oxide sainples containing uran ium was found to be negligible and p resen ted no p rob lem. Samples f ired at t empe ra tu r e s above 1500°C for one hour in a i r exhibited a marked inc rease in "room tempera tu re" emanat ion r a t e s . The predic ted l a t t i ce -loosening t e m p e r a t u r e of meta l oxides is approximately one-half thei r absolute melt ing point. Above this t e m p e r a ­t u r e , sufficient t he rma l agitation is induced to pe rmi t exchange and possibly pe rmanen t displacement of a toms in the c rys t a l l a t t ice .

Therefore , firing these oxide p repara t ions at t em­p e r a t u r e s above 1500°C probably resu l t s in la t t ice defects throughout the c ry s t a l s t r uc tu r e , with the surface defects contributing to an i nc r ea se in surface a r ea and a c o r r e ­sponding inc rease in the emanat ion ra t e .

1. INTRODUCTION

The use of an aqueous s l u r r y of thorium oxide-uranium oxide as ci culating fuel in t he rma l b r e e d e r r eac to r has long been recognized as an in teres t ing possibi l i ty . There a r e many predic ted advantages to a sys tem of this type. On the other hand, however , many quest ions a r i s e in connec­tion with the feasibil i ty of using a pa r t i cu la r type of s lu r ry ma te r i a l as the c i rculat ing fuel. These quest ions usual ly per ta in to such p rope r t i e s as

settling c h a r a c t e r i s t i c s , flocculation, par t ic le shape, par t ic le s ize , absorpt ion c h a r a c t e r i s t i c s of the s lu r ry m a t e r i a l , co r ro s ion -e ros ion effects, f ission product r e l e a s e , and the rma l and radiat ion stability of the s lu r ry m a t e r i a l . To obtain a useful understanding of any one of the above-mentioned c h a r a c t e r i s t i c s it is very essent ia l that ce r ta in common physical p rope r t i e s of the s lu r ry m a t e r i a l be known. One of these p rop ­e r t i e s , which usually r equ i r e s severa l hours for a single determinat ion, is surface a r e a .

The purpose of the work covered in this r epo r t was to evaluate a modified emanation method for determining surface a r e a s of thorium oxide and thor ium oxide-uranium oxide p repa ra t i ons .

The emanat ion method differs from other known methods in that a complete a lpha-par t i c le spec t rum of the emanation (Rn^ °) and its daughter products can be observed, thus enabling p r e c i s e background or "de­posi ted act ivi ty" co r r ec t ions to be made . The r e su l t s of this study w e r e then used in an a t tempt to obtain some relat ion between emanating power and its changes and specific surface and i ts changes.

The samples used in this study were powders of thor ium oxide and some mix tu re s composed of thor ium oxide-uranium oxide with the uranium content being-^^ 10% by m a s s .

The f i r s t s e r i e s of samples consis ted of thor ium oxide p repara t ions fired for the same per iod of t ime at different t e m p e r a t u r e s ranging from 225°C to 900°C. Then, m e a s u r e m e n t s of surface a r e a of these samples were made by the emanat ion technique. These values were compared with those obtained by using the Braunaur , Emmet t and Tel le r (BET) naethod (see Appendix A). It was found that in each case the surface value by the emanation technique was l e s s than the value obtained by the BET method. Also, it was found that the deviation between the values obtained by the two methods dec reased with increas ing firing tenapera ture .

With a fur ther i nc r ea se in firing t e m p e r a t u r e , the two values ap ­proached one another and differed by a very smal l value.

The second and th i rd s e r i e s of samples , a lso of thor ium oxide, were f ired at given t e m p e r a t u r e s , 500° and 900°C, with the per iod of firing var ied up to sixty-four hours . Again, m e a s u r e m e n t s of surface a r e a were made by the emanation technique and compared with those obtained by the BET method. In these ca ses it was found that l a rge reduct ions of surface a r e a took place during the shor t heating pe r iods up to about seven hours . Longer heating pe r iods , up to sixty-four hou r s , produced only slight additional de­c r e a s e in surface a r e a . In these c a s e s , the values of the surface a r e a s obtained by the two methods differed from each other by a constant mul t i ­plicative factor .

The fourth s e r i e s consis ted of samples of a thorium oxide-uranium oxide mix tu re . These were each f i red at different t e m p e r a t u r e s for the same length of t ime and thei r surface a r e a s measu red by the two methods. The p resence of Rn^^^ (with a half-life of 3.82 d) p resen ted no problems in connection with the alpha counting. The samples f ired above 1450°C showed an inc rease in surface a r e a , as de te rmined by the emanation method. This apparent i nc rease is in ag reemen t with the "lattice loosening theory" of Tammann.( l )

2. SAMPLE PREPARATION

Since the m a t e r i a l under investigation was thorium oxide, there was no doubt as to hoinogeneous dis t r ibut ion of the parent of the radioactive iner t gas . Both thor ium nuclides (Th^^^ and Th^^^) of which the oxide is formed furnish ThX by na tura l decay. This conveniently e l iminates the problem of incorporat ing an active parent in the ma te r i a l by the usual method of coprecipi ta t ion.

The problem of the geomet ry of the pa r t i c l e s was simplifed by the method used for thei r prepara t ion . l^ ) A n i t ra te - s tab i l i zed thoria sol was a tomized in a column of gaseous anhydrous ammonia . The result ing m a ­te r i a l was col lected from the bottom of the column, washed with 6-8 normal ammonium hydroxide, then with methyl alcohol, and then fired.

An e lec t r i c furnace equipped with a t empera tu re control ler was used for the f ir ing. The furance was slowly brought up to the p r e s c r i b e d t e m p e r ­a tu r e , held at this t e m p e r a t u r e for a given per iod of t ime , and then turned off. After the furnace had cooled to room t empera tu re , the sample or samples were removed, t r a n s f e r r e d to a weighing bott le , and s tored in a des icca tor .

Examinat ion of the m a t e r i a l produced in this manner has shown that only about 2% is nonspher ica l (see Fig . 1).

All m a t e r i a l for this exper iment was screened, and the fraction p a s s ­ing through a NBS No. 100 sieve and re ta ined on a No. 325 sieve was used.

3. PROPORTIONAL COUNTER

Figure 2 shows a pe r spec t ive drawing of the detector used for the continuous flow m e a s u r e m e n t s of thoron. Detailed information on its con­s t ruct ion is given by Gat rous i s and Crouthamel. l^) The only modification was the use of a one -mi l ins tead of a 2 -mi l cen te r w i r e , permit t ing the counter to be operated at a lower voltage (850 volts) . A modified (Los Alamos model 100) p re -ampl i f i e r was connected di rect ly to one of the Lucite end blocks of the counter . The output from the p re -ampl i f i e r was

passed to an (Argonne type A-61) l inear amplifier and then to a 256-channel analyzer . F igure 3 is a block d iagram of the electronic c i r cu i t s , counter, and sampling sys tem.

2000 X

J

SPHERICAL FIRED FOR

PARTICLES OF 1 hr AT 550

FIG. 1

THORIUM °C

OXIDE--URANIUM OXIDE

Operation of the counter was as follows: The counting gas mix ture (P-IO), 90% argon and 10% methane, was supplied from a commerc ia l gas cylinder at a constant, p rede te rmined flow ra te . As the gas passed over the thorium oxide and out of the sample chamber , it c a r r i e d with it the emanation (Rn ) from the thorium oxide, which then went direct ly into the counter. The alpha pa r t i c l e s result ing from the decay of thoron in the counter expended their energy by ionization of the counting gas . In the 90% argon-10% methane mix tu re , about 30 ev of energy a re spent per ion pair formed. The operating voltage of the counter was below the p r o ­portional region and no multiplication near the center wire occur red .

The c o u n t e r t h u s o p e r a t e d a s an i o n i z a t i o n d e t e c t o r . H o w e v e r , the n u m b e r of ion p a i r s f o r m e d by a g iven a lpha p a r t i c l e , and consequen t l y the s i ze of the p u l s e fed to the 2 5 6 - c h a n n e l a n a l y z e r , w a s p r o p o r t i o n a l to i t s e n e r g y .

LUCITE, OM FILM BMUAU

nkFniJE-imniBun.^ FHENOLie RESIN

(0.062 in. Mkll)

aAS IK

INLESS STIEL WIRE (O.OOI in.)

DOUBLE KDVAg INSULATOR

FIG. g

CYLINDRICAL GEOMETRY PROfORTIOHAL SPECTROMETER

£-^

A (P-IO)Sos Cyli B Regulator

C Voivs D Somp E Propf^tional

F Flow Meter S Vent

.^"'^

r

-®—

PRE AMP

A - 6 1

AMPLIFER

H V. POWER

SUPPLY

256-CHANNEL

ANALYZER

[

FIG. 3

BLOCK DIAGRAM OF ELECTRONIC CIRCUIT, COUNTER, AND SAMPLING SYSTEM

Examination of the thoron decay scheme (see Fig. 4) shows that severa l of the daughters also decay by alpha emiss ion. These daughter products a r e not gaseous and contribute to the so-ca l led "deposited back­ground" of the counting chamber . A method of cor rec t ing for this activity will be discussed l a t e r .

Figure 5 shows a t r ace of a typical alpha spectrum, obtained with the counting sys tem discussed above. The t r ace of this spect rum is also evidence of the relat ively modest but very useful resolut ion (3-4%) that can be obtained with the simple and inexpensive alpha spec t romete r used in this work.

86

X 6.262 ll«v

0.1Sgs

* Pa!

1 82

j 10.

12

ei<

83

( 60.5«

Po2l2

I O - ' B

ii 6.086 I27t) 6.0»7 ! 6 9 t )

I_

3.1»

Pb!08

92

s t a & ' e

DA..GHTERS

,1 •,

i H

Fis. n I THORON DECAY SCHEME A»D ALPHA ENERGIES !

f i a . 5

TYPICAL EMAHATiON SPECTRUM ?mM

1 THORIUM OS IDE

4. OPERATING CHARACTERISTICS OF THE SYSTEM

Statistical considerat ions make it des i rable to observe the maximum number of counts per unit of t ime from any given sample . In this system the counting ra te is a function of the flow rate of the argon-methane mix ­ture . An excessively high flow rate will have a dilution effect on the thoron and will also t r anspor t a la rge fract ion of it through the counter before decay occurs . An excessively low flow rate will pe rmi t a l a rge r fraction of decay to occur before the thoron has reached the effective counting zone.

11

In o rder to es t imate what flow rate should be employed, the resu l t s of W. B. Silkerl"*/ were used. He has shown that the theoret ical flow ra te for obtaining maximum thoron decay in a counter in a continuous flow sys -tein can be calculated in the following manner . Assuming l inear flow in the sys tem, Vj and V2 being the volume of the sample chamber and the counter , respect ively , and substituting volume flow rate for t ime, the equation he employed is given a s :

N = N , ( e - ' ^ ^ ' / ^ - e - ' ' < ^ - + ^ ^ ' / ^ ) , (1)

where

N = the number of thoron atoms decaying in Vj,

No = the number of thoron atoms initially present ,

X - the decay constant for thoron (in rec iprocal minutes) , and

F = the flow rate (in cm^/minute) .

Then, in o rde r to de termine the flow ra te for maximum thoron decay, the following equation is solved for F :

dN . , ^ e- ^ V i / F „ ^-(V^+Vz) e- A(VI + V J / F p2 - ^

= 0 . (2)

It was found that

XVz in [1 + (V2/V1)] (3)

Equation (3) gave, for the apparatus used, a numerical flow rate of 396 cc /min as against the experimental ly determined value of 235 cc /min . F igure 6 is a plot of the experimental ly determined counting ra t e s observed at var ious in tervals of increas ing flow of gas through the counter.

The saine discrepancy between the calculated and experimental values has been observed by Silker(4) and was at tr ibuted to incomplete mixing of the gas s t r eam in the counter .

F rom Fig. 3 it can be seen that, when the system is opened to in­troduce a sample, the counter can be isolated from the r e s t of the system to prevent a i r from entering the counter. After the sample is in place, the sample chamber is closed, vented, and flushed with counting gas for about 5 minutes to sweep out the a i r . Then the vent is closed and the other valves a r e adjusted to pe rmi t the flow of gas leaving the sample chamber to enter the counter . Eight minutes of flow were requi red for the radon-bear ing gas to come to equil ibrium in the counter.

i^m

n©

c m

^ ag© e 8

S 3M

320

300

50 100 ISO 200 260 380

SAS FLOW, c e / n i i n .

COUNT RATE AS FIG. 6

A FONCTION OF GAS FLOW

Although the design of the sample chamber is relat ively s imple, a few comments about it a r e in o rde r at this point. At the beginning of this work, a chamber having one gas inlet and one outlet por t was used. The outlet por t was located in the center of the chamber cover and the sample planchet positioned on the base plate direct ly beneath this port . The single inlet por t was located in the base plate about one inch from the c i rcu la r a r ea covered by the planchet. With this design, it was noted that a sample counted severa l t imes , under the same conditions except for its position in the chamber with respec t to the gas inlet and outlet p o r t s , gave a var ie ty of counting r a t e s .

It was assumed that this problem was due to incomplete mixing of the gases and cor rec t ion was made by redesigning and building a new chamber . The new design entailed reducing the volume of chamber and insert ing a total of four inlet por t s and nine outlet por ts in posit ions in the chamber to provide the neces sa ry turbulent flow. With this design, reproducible counting ra tes were obtained from a given sample i r r e s p e c ­tive of its position in the chamber .

5. THEORY OF THE EMANATION PROCESS

The theory of the emanation p r o c e s s is given in considerable detail in the publications of Flugge and Zimmensw) and Z immensV" ' ' ' ° / . The following discussion covers only those theoret ical details which a r e s ig­nificant to this particxxlar study.

Emanating power E has been defined as the fraction of radioactive i ne r t -ga s a toms formed in a solid that escape from the solid. Zimmensl") has shown that the i ne r t -ga s atom naay escape from the solid ei ther by r e ­coil or by diffusion, so that

E = E R + E D . (4)

If one is able to reso lve these two fac to r s , then it is possible to calculate the surface a r e a of the solid by the use of the following re la t ionship:

• 0 /

v/here

R = the recoi l range , and

TQ - the radius of the p a r t i c l e s .

F o r spher ica l p a r t i c l e s , for which r o » R , equation (5) reduces to

„ R / sur faced / . . ^R = T P\ J • (^)

^ 4 V m a s s / The der ivat ion of this re la t ionship is given in Appendix B. In this study all emanation m e a s u r e m e n t s were made at room t e m p e r a t u r e , and the t empera tu re -dependen t diffusion effect (Ej)) was considered negligible.

One of the l imit ing fac tors in the in terpre ta t ion of the emanation data obtained in this work was the determinat ion of the ra te of formation of the i n e r t - g a s a toms in the solid. The continuous flow of counting gas a c r o s s the sample as used in this study, unlike the Hahn(9) technique, does not lend itself to the measu re raen t of the emanating power direct ly . Therefore , the ra te of format ion of the i n e r t - g a s a toms had to be found by some other m e a n s , since only the ra te of escape of thoron could be accura te ly de te rmined by alpha counting.

F r o m the decay scheme of Th "* shown in Fig . 7, it is apparent that when thor ium is separa ted from monazi te or thori te the two isotopes, Th^''^ and Th a r e obtained. Except for c a s e s where ex t reme puri ty is des i red , the thor ium at this point is essen t ia l ly "daughter f r ee , "

If the separa t ion t ime of the thor ium is known, that i s , the t ime when secu la r equi l ibr ium is des t royed by the separa t ion of Th^^^ and Th^^^ from their daughter p roduc t s , then the ra te of formation of the ine r t -gas a toms can be calculated. By employing the Bateman(lO) equation

N = Ao (h^e"^A* + hge" '^B* + h^e -^C^) , (7)

where AQ is the number of Th atoms initially p resen t and X^, Xg, and X Q a r e the decay constants of Th^^^, Ra^^®, and Th^^®, respect ively, and the d imensionless functions of the decay constants have the following systematic form:

XA ?^B A XQ - X^ Xg - X^

hi. = ^A XB

• ^ A - ^B ^ C - ^B (8)

^A Xi

^ ^ A " '^C '* B - ^ C

,232 the thoron activity, due to buildup from Th , can be calculated for any t ime t after separat ion. Likewise, the thoron activity due to the natural decay of Th at any t ime t after separat ion can be calculated after a value for N at tg has been determined, in which N r ep re sen t s the number of Th^^^ a toms initially p resen t at t ime of separat ion.

Th"2

00

1 .ijxio' "y

a

Ra2S8

88 S.7» /

Ae"8 89 S.Ih

a/

/

/

Th228 90 1.9y

88 3.6d

-t. R n " 0

18 6i|s

FIG. 7

THORIUM OR l|n SERIES

Figure 8 is a plot of the change in thoron activity with t ime. The calculated values a re based on one g ram of daughter-free thorium having the natural rat io of Th^^^ to Th ^® at t ime tg. It should be noted that the thoron activity r eaches a minimum value at approximately 4.5 ye a r s after the thorium separat ion, then i nc rea se s to approach the secular equilibrium value as an asymptote . An approximate value for thoron decay can be ob­tained by taking the sum of the two points on the curves at any time t after separat ion.

OS

o t-

o

^ o

1®«

I©»

! 1 1 1

^ S i 2.H X 105

- \ _ \ y^ ~~ X r ~" / \

/ V

1 1 ! 1 1

•:'"'| ! 1 1 1 ' 1 M 1 1 ' 1 ! • ^ D/M Rn220 DUE TO IUIL0UP FROM

^ — T I M E .

y ^ 0 '^ t

2 4 6 8

/ - - B / M R i ) 2 " DUI TO ^ °

RESIOy^l Th228 ( t = 1 .9 ,5 30 V " ' 40

\ 1 l\l 1 1 i 1 1 1 1 1 1 1 1

! ' 1 ' 1 ' T h « " ( t , ; j = I .

•pT -

4 K I 0 ' % )

PER GEHT OF E 9 U ( L B . D l S l N T E B R A T I O t l HATE

_ ™

7 1 . I 5 4 . 2 4 0 . 0 4 0 . 8 4 6 . 9 5 3 . 7 8 2 . ® 9 3 . 7 S 7 , 8 9 9 . 0

1 1 1 1 1 1 J_J 12 16

TIME, IT 20 ^^

FIG. 8

THORON ACTIVITY AT TIME t AFTER THORIUM SEPARATION

28

6. RECOIL RANGE OF Rn^^°

The atomic stopping power of a substance is generally assumed to be the same for recoi l a toms as for alpha pa r t i c l e s . Then, by employing the values of Livingston and Be the ( l l ) and applying the appropriate cor ­rect ion factors for density, atomic or molecular stopping power, and so on, the recoi l ranges in different ma te r i a l s can be calculated. For example, a range in thorium oxide, R^hO ' ® given in t e r m s of the range in a i r :

^ThOz - ^ a i r p (9)

where Aair i^ the "atomic weight of a i r , " that i s , the square of the weighted average square root value: ( 0 . 8 v ^ + 0.2^^16]^ = 14,4 The value of A for compounds and mix tu res a r e handled in the same way.

16

Flugge and Zimmensl^) e s t ima ted the recoi l range of thoron by employing the express ion

R = G™ - ^ , (10)

where G is a proport ional i ty constant , p is the density of the solid, and (AW/s) is the average ra t io of the atomic weight to the atomic stopping power, re lat ive to a i r , of the a toms in the solid. Ei ther of these methods may be used to calculate the range of recoi l emanation in lieu of the lack­ing exper imenta l m e a s u r e m e n t s .

In this study Eq. (9) was employed. If R in Eq. (6) is replaced with the express ion for R ^ h o given in Eq. (9), then the equation for surface a r ea reduces to

4Ej^(mass) Surface r i , (11)

R

where R^ is the " recoi l range factor" for thoron in Th02 and equal to

/•^ThO R - Ra.ir P a i r y ^ • ~ ^ThOg '^ThOg • ^^^^

Fu r the r d iscuss ion of recoi l range is given in Appendix C,

7. DETERMINATION OF RECOIL EMANATION BY a COUNTING

The decays of Rn^^° and of i ts daughter products include four nuclides that involve alpha emiss ion : Rn^^°, Po^^^, Bi^^^, and Po^^^. During the normal opera t ion of the counter Pb^^^, from the decay of Po^^ , becomes deposited on the inner surface of the counting chamber . This deposited m a t e r i a l decays by beta emiss ion , with a 10.6-hr half-l ife, to Bi^^^ and finally to Po^''^, both of which a r e alpha e m i t t e r s . If the counting is s ta r ted in a re la t ively clean counter , the "deposited background" will r emain prac t ica l ly negligible for severa l hours . However, even a low background may r e p r e s e n t an apprec iable percentage of the total activity when the emanat ion from a pa r t i cu la r sample is low. Therefore the fol­lowing method was employed for making background co r rec t ions for all emanation m e a s u r e m e n t s made in this study.

Let it be a s sumed that the counter has been in constant use for sev ora l days and that the re is a cons iderable amount of deposited activity p re sen t in the counter . The counting gas is d iver ted to bypass the sample chamber and pas s only through the counter, with the gas flow ra te and all other operat ing conditions maintained constant . A m e a s u r e m e n t is made

of the deposited activity, and the peak- to- to ta l rat io for Po^^^ is determined over a given energy span. The energy span from 5.5 to 9.0 Mev, that was observed was chosen to include the energies of the Rn^^°, Po^^ , Bi^^^, and Po^^^. Figure 9 shows a typical spec t rum from "deposited background" activity only. Several de terminat ions of the peak- to- to ta l rat io gave values that agreed within 14 per cent. The background cor rec t ion is then made by determining the counts under the Po^^^ peak (8.77 Mev) obtained from the composite alpha spec t rum from a sample. These counts a r e then con­ver ted to background activity by dividing by the peak- to- to ta l ra t io . This background is subtracted from the counts, totaled over the same energy span, i .e . , 5.5 to 9.0 Mev, that were obtained from the sample . It should be noted that the total activity minus background activity r ep re sen t s the activity due to both Rn^^" and Po^ and mus t be taken into consideration when calculating Ej^. The resu l t s of eight ten-minute counts collected at in tervals over a s ix-hour period, while active gas was continuously flow­ing through the counter, a r e shown in Appendix D.

1 US

5 em

90

80

70

80

SO

40

30

20

10

-

-

-

-

~

[ i i

1

S

% i

J1

BACKGROJND ACTIVITY FROM RnZ20 DAU6HTERS IDIV=0.28Mev

#

I

a.

I 1 ; [ ! i 1 i I 1 1 ! [

ENER8Y —

F IG . 9

ALPHA SPECTRUM OF DEPOSITED BACKGROUND ACTIVITY

1 L 1

8. EMANATION MEASUREMENTS

The f i r s t set of m e a s u r e m e n t s was made on a group of Th02 sample fired at t empe ra tu r e s ranging fro3xi 225°C to 900°C for a period of two and one-half hours . A smal l (approximately 200 mg) portion of each sample was weighed out and used for the determinat ion.

In Table 1 a r e shown the specific surface values obtained from the emanation m e a s u r e m e n t s employing Eq. 11. The re la t ionship between these values and the absolute surface a r e a values obtained by the BET method will be d iscussed l a t e r .

Table 1

CHANGE IN E R AND SURFACE AREA AS A FUNCTION OF FIRING TEMPERATURE

Fi r ing Temp,

°C

225 350 500 650 650 650 900 900

E R . P e r Cent

10.2 6.8 4 .6 2.1 2.0 2.2 0.080 0.076

Surface Area , m Y g m

1.1 0.74 0.50 0.22 0.21 0.23 0,0085 0,0082

Figure 10 is a semi logar i thmic plot of the data in Table 1. Between 225°C and 650°C the emanating power E R can be de termined from the equation

E R = 18.32 e™°'°3ix ^ ^13^

where x is the firing t e m p e r a t u r e (°C). Above 650°C the " room t e m p e r a ­ture curve" drops sharply and at 900°C reaches 0.08 pe r cent„

The compara t ive ly high emanating power value of the 225°C-fired sample is indicative of the t remendous ly l a rge surface a r e a s developed in thor ium oxide "hydroge ls . "

The curve shown in Fig. 11 was plotted from the firing t empe ra tu r e v e r s u s the pycnometr ic density data of Foex.(12) These data show that a considerable change of surface a r e a can be expected with f ir ing, up to t e m p e r a t u r e s of about 900° to 1000°C.

F igure 12 is a plot of the firing t empe ra tu r e v e r s u s specific surface a r e a ( m y g m ) showing the re la t ionship between the surface values obtained by both the emanat ion and BET methods . The curves c lear ly show that the two raethods a r e not equally sensi t ive to the surface changes occurr ing over the firing t e m p e r a t u r e range f rom 250°C to 900°C. As the firing tem.pera-t u r e s i nc r ea se , the BET method detec ts a p rog re s s ive ly g r e a t e r d e c r e a s e

of surface a r ea than the emanation method. In the vicinity of 900°C, the difference between the two values of surface a rea appears to be approach­ing a minimum value.

Q.

—

[—• •

p-4

1

-

—1

—

1

^ '

1 1

1

\

\

200 HOC 600 800 FIRING TEMPERATURE, °C

FIG. 10 CHANGE OF RECOIL EMANATION FROM THORIUM OK IOE AS A FUNCTION OF FIRING TEMPERATURE

The following argument is offered as a plausible explanation of this interest ing phenomenon. With each firing at a higher t em­pe ra tu r e , shrinkage and s t ruc tura l changes begin to have a pronounced effect on the porosi ty of the a m o r ­phous thorium oxide pa r t i c l e s . The surfaces of ext remely small deep po re s , which served as adsorption si tes for BET m e a s u r e m e n t s , a re now ei ther great ly reduced or com­pletely el iminated at the higher f i r ­ing t e m p e r a t u r e s .

1000

I 800

I

8 8 . 2

PYCNOMETRIC DENSITY, gn ™^

CHANGE

FIG IN DENSITY AS

TEMPERATURE. (FIRING

li A FUNCTION TIME - 1 h

OF )

FIRING

1000

100

0 . 1 ^

300 500 700 900

FISING TEMPERATURE, "C

FIG. 12 SURFACE AREA CHANGE AS A FUNCTION OF FIRING TEMPERATURE. (TIME AT HEAT = 2.5 hr)

20

The d e c r e a s e in porosi ty has only a small effect on the emanation measu remen t . This is unders tandable because the emanation method does not detect the t remendous in ternal surface of the porous pa r t i c l e s . However, a reduction in that f ract ion of the total porosi ty which is p r e sen t in the outer or skin of the pa r t i c l e r e s u l t s in a sma l l e r surface a r e a change, which the emanation method does detect .

Therefore , over the firing t e m p e r a t u r e range f rom 250° to 900°C, in which in ternal poros i ty is being e l iminated or reduced to the point where the BET adsorba te cannot r each the adsorpt ion s i te , a l a r g e r d e c r e a s e in surface a r ea can be expected to be m e a s u r e d by the BET method than by the emanat ion method.

A second s e r i e s of m e a s u r e m e n t s was made to de te rmine the effect of firing t ime on the change in surface a r e a . A firing t e m p e r a t u r e of 500°C v a s selected because it was jus t below the t empera tu re range where the mos t pronounced surface changes occur red . Therefore , it was expected that prolonged heating at th is lower t e m p e r a t u r e , 500°C, would produce the same surface changes a s a shor te r firing at a higher t e m p e r a t u r e . However, the data f rom this s e r i e s of m e a s u r e m e n t s show that ve ry l i t t le surface a r ea change occurs after the initial 2 .5-hour firing per iod. This holds t rue for firing t i m e s up to 64 hou r s , a s shown in Table 2.

Table 2

CHANGE IN E R AND SURFACE AREA AS A FUNCTION OF FIRING TIME

AT 500°C

F i r ing Time,

hr

2.5 7.5

15.5 44 64

E R . P e r Cent

4 . 5 * 4 . 3 * 4 .0* 4 .0* 4.4

Surface Area , m Y g m

0.49 0,47 0.44 0.44 0.48

•Average of two or m o r e m e a s u r e m e n t s

F r o m an extrapolat ion of the cu rves in Fig. 12, the surface a r e a of all the s tar t ing m a t e r i a l used in the work descr ibed in this paper is a s sumed to be approximately 1,2 rc^/gm and 200 m y g . This would be as de te rmined by the eraanation method and the BET method, respec t ive ly , and p r i o r to any heat t r ea tmen t .

100 s = p q =

= 10

"•' I i I L J L J LJ I

ZZEil :

0 EMANATION VALUES

1 BET VALUES

^

10 20 aO ItO 50 60 70

T I M E , h r

F I G . 13

CHANGE IN SURFACE AREA AS A FUNCTION OF

F IRING TIME AT 600»C

The emanation values plotted in Fig, 13 a r e in very good agreement with the BET data in the sense that they differ a uniform constant factor.

The third se r i e s of m e a s u r e ­ments was again a study of the change in surface a rea with firing t ime, but at 900°C. The data in Table 3 contain the measu remen t s made up to a firing t ime of 15 hours . Plots of these data along with some corresponding BET values a re shown in Fig. 14. The in­teres t ing point to note here is that a considerably longer firing time is r e ­quired before the point is reached where a negligible decrease in su r ­face a rea occurs with further firing. At 900°C, the time required to reach the leveling-off point is ^ 9 hours .

Table 3

CHANGE IN E R AND SURFACE AREA AS A FUNCTION OF FIRING TIME

A T 900°C

Fir ing Time,

hr

2.5 7.0

15,0

ER. P e r Cent

0.080 0.016 0.011

Surface Area , m Y g m

0.009 0.002 0.001

A fourth se r i e s of samples , consisting of thorium oxide-uranium oxide (10% U), was p repa red and fired according to the procedures p r e ­viously descr ibed. The firing t ime for this se r i e s was held to 1 hour and the t empera tu re var ied between 650° and 1750°C.

A pre l iminary examination of this mate r ia l by alpha counting showed that there was no detectable interfering alpha contribution from Rn^^^ (ti/2 = 3.82 d).

Because of the lower emanating power of the h igh- tempera tu re -fired m a t e r i a l , the sample size used for counting was increased to about 1 g ram. Four - inch d iameter aluminum planchets were used so that the

22

sample thickness on the planchet could be kept to a minimum. The per cent emanation due to recoi l ( E R ) and the surface a r e a , as calculated by Eq. (11), a r e given in Table 4. Data a r e shown in Fig. 15.

0.1

0.001

t 1 ™

_

1 1

1 r J-1

K 1

1 1 1 1 1 i 1 i 1 — 1 . * ~

: 1 0, a EMANATION VALUES _ 1 i I BET VALUES _

*.

1

. - X . , j _ _

•——o^

1

y-MO-e

^ ^ s o o - e

r-9O0°C

1 1

—

T = 1 — ^

—

"

~

—r-8 10

TIME, hr 1» 16

Fie, l« CHANGE IN SURFACE AREA AS A FUNCTION OF FIRING TIME AT 900°C

Table 4

CHANGE IN E R AND SURFACE AREA OF ThOz-UOz AS A FUNCTION OF

FIRING TEMPERATURE

Fir ing Temp, °C

650 1200

1200 (for 2 hrs) 1200 (for 2 hrs)

1400 1600 1750 1750

E R ,

P e r c e n t

2,0 0.031 0,019 0.020 0.033 0.090 0.34 0.34

Surface Area,

mYg

0.22 0.0034 0,0021 0,0022 0.0036 0.0096 0.037 0.037

F r o m par t ic le size dis tr ibut ion and density data on a thorium oxide-uranium oxide sample f ired at 1200°C, the calculated surface a r ea , a s s u m ­ing zero porosi ty and perfect sphe re s , was 0.01 mYg- An explanation of this apparent d iscrepancy will be given in Section 9.

23

» ~^

g 0.01

0.001

J BET VALUES "

0 EMANATION VALUES "j

Q«-2 hr AT HEAT

1200

FIBIHO TEMPERATURE, °C

1800

FIG. IB SURFACE AREA CHANGE AS A FUNCTION OF FIRING TEMPERATURE FOR ThOg - UO2 SYSTEM. (FIRING TIME: I hr)

It may be seen from Table 4 and Fig, 15 that an increase in surface a rea appears to occur in ma te r i a l fired above 1500°C, At 1750°C, the magnitude of the inc rease of surface a r e a is certainly beyond the l imits of any reasonable probable e r r o r that we might ass ign to the emanation m e a s u r e m e n t s .

9. SUMMARY

1. A study was made of the emanation method for determining the surface a r ea of spher ical thorium oxide par t ic les using a cylindrical geom­etry proport ional spec t romete r and a continuous-flow counting system to m e a s u r e the a lpha-par t ic le decay of the recoi l emanation from var ious thorium oxide p repara t ions .

2. The data c lear ly show that d i rect in terpreta t ion of E R values from the thorium oxide p repara t ions , in t e r m s of surface a rea , does not resul t in values that agree with the "absolute" values obtained by the BET method.

3. Agreement can be es tabl ished between the two methods by ap­plying two cor rec t ion factors to the emanation surface values. The f i rs t factor, Cj, c o r r e c t s for the efficiency of the counter and for decay losses occurr ing in the sys tem before and after the effective volume of the counter.

24

By applying the following reasoning to the data on the high-fired thor ium oxide-uranium oxide p r epa ra t i ons , a value for Cj was obtained. The surface a r e a va lues , obtained by both the emanation and BET methods , reach a min imum at 1200°C. This would indicate that the porous s t ruc ture of the p repara t ion was completely dest royed. To verify th is , the specific surface a r e a of the 1200°C-fired m a t e r i a l was calculated. This calculat ion was based on pa r t i c l e size dis t r ibut ion data, and perfect nonporous spheres with a density of 9.8 gm/cm^ were a s sumed . The computation resul ted in a specific surface of 0.01 m y g m , as compared to the 0.03 m y g m actually found.

Therefore , in the case of this sample f i red to 1200°C, both the emanation and BET method detect the same external or geomet r ica l s u r ­face. However, the emanat ion value is l e s s than the BET value by a factor Cj. In this study C^ was found to have a numer ica l value of ' ^8 .7 .

The second factor , Cj , c o r r e c t s for what might be t e r m e d the increas ing efficiency of the emanat ion method that occu r s when the p o r o s ­ity of the araorphous oxide is reduced by firing. The value of this factor will be some function of the fir ing t e m p e r a t u r e , firing t ime being constant. It can be obtained f rom the cu rves plotted f rom both emanat ion and B E T data on at l eas t th ree samples f i red over a w e l l - s p r e a d t e m p e r a t u r e range , i .e . , 200°C, 6 0 0 X , and 1000°C.

It should be made c lea r that the ca l ibra t ion curves or the ex­p r e s s i o n for C2 der ived f rom them is only applicable to a pa r t i cu la r study, that i s , data from, p r epa ra t i ons f i red for two hours at va r ious t e m p e r a t u r e s cannot be eroiployed in a study where the firing per iod is to be five hour s .

However, once the n e c e s s a r y bas ic data has been obtained for a pa r t i cu la r study then numerous m e a s u r e m e n t s can be made and specific surface values calcula ted in a f ract ion of the t ime requ i red to make a single BET m e a s u r e m e n t ,

4. The inc rease in surface a r e a occur r ing at t e m p e r a t u r e s above 1500°C indicates that emanating power data furnishes a c lea r index of the t e m p e r a t u r e s at which reac t ions in the solid state may be expected to take place. The nature of the physical changes occur r ing in the m a t e r i a l f i red above 1500°C that effect a surface i nc r ea se is uncer ta in .

5. A la rge fract ion of the i nc r ea se in surface a r e a of the t h o r i a -urania p r epa ra t i ons f i red above ISOO' C can be accounted for by "lat t ice loosening." The t e m p e r a t u r e at which lat t ice loosening occu r s was de ­fined by Tammannl-'-) as the point of incipient softening. It is apparent ly the t e m p e r a t u r e at which reac t ions in the solid state become opera t ive .

25

6. The rat io of the lat t ice loosening or " Tammann t empera tu re " to the melt ing t e m p e r a t u r e usually r e su l t s in values lying between 0.5 and 0.6, if an absolute t e m p e r a t u r e scale is used. F r o m the emanation data obtained in this study, the la t t ice loosening temiperature of ThOg, neglecting the smal l UO2 fraction, was found to be 1460°C or 1733°K. Taking the me l t ­ing point of Th02 as 3050°C or 3323°K, there resu l t s a rat io of 0.52, which is in good agreement with Tammann ' s work.

26

Appendix A

BET LOW-TEMPERATURE ADSORPTION METHOD FOR DETERMINING SURFACE AREAS

Detailed information on the theory and exper imenta l technique of the BET method can be found in a wide var ie ty of text books.l-'-^'-'-'^) How­ever , at this point, a few r e m a r k s about the pr inciple of the method will be of value in unders tanding the in te rpre ta t ion of the data.

The method entai ls selecting from an exper imenta l adsorpt ion i so the rm a point r epresen t ing the volume and hence the number of molecules corresponding to a monomolecular layer of the adsorba te . Then, rault ipl ication by the average c r o s s - s e c t i o n a l a r e a of each m o l e ­cule will yield the absolute surface a r ea .

The accuracy of the method r e s t s upon the exac tness with which the point cor responding to a monolayer of adsorbed molecules can be picked and the c loseness to which one can approximate the average a r ea covered by a molecule of the adsorba te .

Molecular a r e a s corresponding to the packing of inolecules in the liquefied adsorba te a r e in genera l about 20 per cent l a r g e r than those co r ­responding to the packing of the molecules in the solidified adsorba te . Hence, absolute surface a r e a m e a s u r e m e n t s m u s t be r ega rded as unce r ­tain by at l eas t this amount.

All BET m e a s u r e m e n t s cited in this paper were made by the Armour R e s e a r c h Foundation. Ethylene was employed as the adsorba te . However, the m e a s u r e m e n t s should be quite conaparable to m e a s u r e m e n t s by ni t rogen adsorpt ion since the c r o s s section of the adsorbed ni t rogen and ethylene molecu les a r e 15.8 and 17.5 square A n g s t r o m s , respec t ive ly . Thus, the ethylene molecule should be able to pene t ra te mos t of the open po re s and c r ev i ce s access ib le to the ni t rogen molecule . F r o m this we can conclude that the adsorpt ion or BET method can be employed for ei ther porous or nonporous sol ids , and that the surface a r e a obtained will include the inner surface as well as the outer or geomet r ic surface .

Appendix B

DERIVATION OF THE EXPRESSION FOR E R

In this derivat ion it is assumed that the par t i c les a re spherical , with a radius r>10"^ cm., and r » R , where R is the recoil range. Since r is many t imes g rea t e r than R, the i l lustrat ion shown in Fig. 16 is valid. A Rn recoi l atom can escape from the surface of a par t ic le only if its parent l ies within the range R of the surface. Then the fraction of iner t -gas a toms (Rn^^°) formed from paren t s (Ra^^*) lying within the range R from the surface is

surface volume

MB, W CONVEX SUBFACE OF SEOTOR

kRU OF SPHEBE

111'.

« • I V VOLUME j • It V «SS /

p = DENSITY

FIG. 16

RECOIL FROM A SPHERICAL SURFACE WHERE r ^ R

If we next c o n s i d e r a po in t P l o c a t e d a t s o m e d i s t a n c e X f r o m the s u r f a c e of the s p h e r e , w h e r e X i s l e s s t han R, a s be ing l o c a t e d b e t w e e n two p l a n e s a d i s t a n c e R a p a r t , then e a c h Ra decay even t tha t o c c u r s a t poin t P wi l l r e s u l t in a Rn ° a to in r e c o i l t e r m i n a t i n g at the s u r f a c e of a s p h e r e r e p r e s e n t e d by the c i r c l e in F i g . 16. The f r a c t i o n of the Rn^^° a t o m s f o r m e d a t a d i s t a n c e X f r o m the s u r f a c e tha t e s c a p e by r e c o i l i s t hen

27rR (R-X) R - X 4'7TR^ 2R

28

The fract ion that escape by recoi l over all values of X from 0 to R is given by

f^ R-X ^ dx 0 2R 1

Thus the emanating power due to recoi l is

__ R /surfaceA _ R / s u r f a c e \ ^ 4 \ vo lume/ 4 I m a s s /

Appendix C

CALCULATION OF RECOIL RANGE OF Rn^^o

The recoi l range of Rn^^° was calculated by employing the express ion

The value of R^^j. for Rn^^° was a s sumed to be the same as that for alpha p a r t i c l e s , for namely, 8.3 x 10"^ cm, obtained from M. Livingston and H. Bethe.'^-"-/ The other values used w e r e :

ATh02 191

Aai r 14.4

P a i r 1.23 X 10"^ gm/cm^

For samples f i red under different conditions PTh02 takes on a wide range of va lues . The effect of both firing t ime and firing t empera tu re on the density of the resul t ing oxide is thoroughly d iscussed by M. Foex . l l^ i However, in the p r o c e s s of calculat ing the surface a r e a from Eq. (6), we can obtain a value for R-jhO ^ThO which is designated as R^ and which leaves Eq. (11) independent of the density of the thorium oxide sample . In the samples containing both ThOg and UO2 the change in recoi l range due to the uran ium was cons idered negligible and no cor rec t ion was naade.

Appendix D

BACKGROUND STUDY

A peak- to- to ta l rat io of 0.184 was used in the background study cited he re . This value r ep re sen t s the rat io of deposited activity due to Po^^^ to the total deposited activity observed between the energy span from 5.5 to 9.0 Mev.

Figure 17 is a plot of the data contained in Table 5 showing excel­lent agreement among the net cpm values and also showing the rate of in­c rease of deposited background activity.

I

S § 200

g a 3 t 100 2 g

—

_A_

y »

4

'

/

1

_A_^ ,

1

A

/ X -,

i 1 1 I

> *

_ ^ . ^ o

, i

\ r

,

—n.—

—

—

1

5000

MOO

3000 I

2000

1000

5 6 TIME, hr

FIG. 17

CORRECTIOh FOR VARIABLE BACKGROUND ACTIVITY DEPOSITED IM COUNTER

Table 5

NET COUNTING RATE AFTER CORRECTING FOR DEPOSITED BACKGROUND

Time

12:00 12:40 1:15 2:09 3:30 4:30 5:00 6:18

Total between 5.5 and 9.0 Mev

3214 3278 3259 3234 3398 3518 3528 3573

Counts per

Total Due to Po212

15 17 27 41 51 72 71 90

Minute

Deposited Background

81 92 146 222 277 391 386 489

Net, Due to (Rn220+Po2^6)

3133 3186 3113 3012 3121 3127 3142 3084

31

The s tandard deviation in the net counting ra te due to Rn ' and Po'^'' , based on the above data, is 0 = +1.5% or 3115 +47 cpm.

ACKNOWLEDGMENT

I am s incere ly grateful and indebted to Dr. Joseph Ziomek, Dr. Car l E. Crouthamel , Chris topher Gat rous i s , and the other m e m b e r s of Dr . Crou thamel ' s group for thei r many helpful suggestions and discussions throughout the course of this work.

BIBLIOGRAPHY

1. G. Tammann and A. Sworykin, Z. anorg. a l lgem. Chem., 176, 46 (1928).

2. P r iva te Communication from C. Crouthamel and W. Knapp.

3. Applied Gamma Ray Spec t romet ry , ed-, by C. E. Crouthamel , Pe rgamon P r e s s , (i960), p . 84.

4. W. B. Silker , The Determinat ion of Thorium by Propor t ional Counting, HW-32436 Re^T" — " -____————-——— - _ _

5. S Flugge and K. Z immens , Z. physik, Chem., B42, 179 (1939).

6. K. E. Z immens , Z. physik. Chem., A191, 1 (1942).

7. K. E. Z immens , Z. physik. Chem., A191, 95 (1942).

8. K. E. Z immens , Z, physik. Chem., A192, 1 (1943).

9. O. Hahn, and O. MuUer,, Z. E lec t rochem. , 29, 189 (1923).

10. H. Bateman. P r o c . Cambridge Phi l . S o c , 15. 423 (1910),

11. M. Livingston and H. Bathe, Revs. Mod. Phys.,_9, 245 (1937).

12. M. Foex, Soc. Chim. (France) , 55_ ( l6) , 231 (1949).

13. Colloid Chemis t ry , Theore t ica l and Applied, ed. by Je rome Alexander, 5, 434, Reinhold Publishing Co, (1944).

14. P . H Emmet t , Am. Soc ^ Testing Mate r i a l s , 41 , 95 ( l94 l ) .