SELF-DIFFUSION OF Na-22 IN MOLTEN - Digital Library/67531/metadc130565/m2/1/high... · SELF-DIFFUSION OF Na-22 IN MOLTEN PbCl2-NaCl MIXTURES APPROVED \tZS(U^j Major professor U"'/;

SELF-DIFFUSION OF Na-22 IN MOLTEN

PbCl2-NaCl MIXTURES

APPROVED

\tZS(U^j

Major professor

U"'/; &??•

Minor professor

rfAv ^ ^ , 4 . ^ , , , — Director of the Department of Chemistry

Dean of the Graduate Softool

SELF-DlFFUtilON OF Sa-22 IH 10l&BH

fbClg-SaCl MIXTURES

THESIS

Presented to the Graduate Council of the

North Texas state university in Partial

Fulfillment of the Requirements

For the Degree of

MASTER OF SCIENCE

BY

Xmn *aun HSU# B. s<

Denton* Texae

January, 1965

TABU: OF CONTENTS

Pag® LIST OP TABLES.. i *•

LIST OF ILLUSTRATIONS... V

CHAPTER

I. INTRODUCTION 1

II.. EXPERIMENTAL PROCEDURE AND R E S U L T S 1 2

III. DISCUSSION. 30

BIBLIOGRAPHY. 52

ill

LIST OF TABLES

tfttel® Page

I * DHaX It5 «2/s«e in PfcClg-5 • 5 mol®$ »a01 16

II. Djj^xio^ cm2/sec in phcig-10«G mole^ laCl......... if

III, % A*1G5 0ffl2/i«© in ptJClg-sa.O mol®^ saCl.*....... 18

IV, Dga*105 oa2/««o in ybCl^O.O mole£ NaCl 19

V * % ax i o 5 °®2/S0ft 111 *to0l2-45.0 aol* Haci 20

VI, Straigfat-11m Equations for the Various Compo-sitions of Ma#. 21

VII. Straight-line Equations for the Various

Composition of PhCl2 22

VIII. Diffusion Isotherms of sodium 35

IX* Diffusion Isotherms of L e a d . . • 36

X. Diffusion Isotheraa of chloride .. ...,. 37

XI. Calculated Self-diffusion coefficients of Various Molten Salts at the Melting point... 42

j XII. Eleotronic polariaabilities and X for ! Certain Molten Salts 45

!•

LIST OF ILLUSTRATIONS

Figure , page

1# Graph Showing the Depth of penetration of Na-22 in pyrex and vycor « « . . . 14

2# Graph showing Variation of log dAV£.# with l/T for the System pfc01g~5*B »ole# NaCl 23

3* Graph Showing Variation of log D.v«, with l/T for the System pliClg-lO.Onaol©^ HaOl* 24

4. Graph Showing Variation of log DAvft with l/T for the System fbclg-22*o'jlol0^ NaCl* • • • * • 25

5* Graph Showing Variation of log D-va. with l/T for the system FbGlg-JOTO0®©!#^ NaCl 26

6. Graph Showing Variation of log with l/T for the system Pt>Cl2-45»0Pnole^ NaCl 2?

7* Graph showing variation of log with 1/f for Various CoapoaitloiiB of NaCl in PbCLg 2®

8. Grapl Showing the Motivation Energies of sodium, Lead, and Chloride Ions as a Funotiozi of Composition of NaCl in Molten PfcClo-IaCl Mixture . . 33

9» ©lffusloii isotherm® of Sodium Ion at 5CXTC, 550 C, and 600°C 38

10. Diffusion Isotherm® of Lead and Chloride ions • at 500°C» 550 C, and 600°C..* 38

11. se l f -d i f fus ion coeff ic ient of Various Ions at the Molting point as a Function of Melting T®ap®ratur® 43

12. The Difference of Electronic p»lari2iabllity for , -Various Salts 'as a Function of X* • • • • 46

CHAPTER I

INTRODUCE IOH

Although tht t h e o r i e s of gases and c r y s t a l s so?# a t r e -

spec tab ly advanced s t a g e s , a comprehensive t h e o r e t i c a l t re .a t -

steml 0# liquid® la s t i l l under development. Liquids h a f t prop-

er t l e® of both gases and s o l i d s . Accordingly, the t rea tment

of l i q u i d structure theory can be approached from e i t h e r $H#»

and two main l i q u i d structure t h e o r i e s t o r e suggested in 193*7,.

On* was Lennard-jonea wad Devonshire1 a " L a t t i c e Theory" (tO) in

which «a@h molecule l a the l i q u i d was considered t o be

t o the neighborhood of on# of the I n i t i o # s i t e s by the s u r -

rounding molecule® with Interaction f o r ce s r e s t r i c t e d t o th§

n e a r e s t neighbor© w i t h i n the H c e l l w . The other t reatment was

Btmal 1 * "Molecular Theory" ( 1 }. His Idea of l i q u i d s was t h a t

of a "homogeneous, coherent, and e s s e n t i a l l y I r r e g u l a r a s -

semblage" . Both t h e o r i e s have been sub jec ted to modi f ica t ion

(16* 27)> but norm hap proven t o be en t i re ly s a t i s f a c t o r y .

In genera l , t h o " l a t t i c e Theory" la more s u i t a b l e near the

melting point while the "Molecular Theory** Is b e t t e r i n the

v i c i n i t y of the o r i t i c a l point(24)• Recently, more d i r e c t ap-

proaches have been made t o develop the l iquid theory fro® the

fundamentals of ln te rmolecula r fo r ce s (13, 15 )> and s t f t t l i *

t l c a l ffi#c*ianl@s with we l l de f ined approximations (18}# When

2

ccmpared with the exjierlmental data, the results have b»«n

•noourAging*

Fused salts are liquids of specific typt# They differ

from all other classea of liquids la that they contain In the

concentrated form positIvely and negatively charged particles,

which result In their electrical conductivity, prom X-ray and

neutron diffraction measurements, it has been found that there

1® a high degree of short-range order In the melt hut no long-

ran®® order* The coordination numbers are always smaller than

those of solid crystals, and the molar volumes are about twen-

ty per cent larger* Thus, the empty volume Is Increased then

solid crystals melt* This empty volume provides a Ȥbml&m

for transport properties such as electrical conductance,, ther-

mal conductivity# viscosity, and diffusion.

Various model® have been applied t© ionic melts(4v 22).

Hole model(modified lattice model) had considerable success#®

In estimating activation energies(6, 1, 26, 31)• The signifi-

cant structure model has been extended and also applied to

molten KCl with success(3)» Ability of various models of ionic

liquids to predict data has- been dlscussed(4). Nevertheless*

these models do not give complete and satisfactorily quanti-

tative agreement with the experimental data on self-diffusion.

Moreover, at present, there are other factors that make the

quantitative testing of the proposed models difficult. Large

errors and rather scanty experimental data are typically found*

Part of the variation Is llHely due to the employment of several

experimental methods.

$he experimental methods applied to establish the struct-

ture of tilt ionio liquids have included their transport prop-

erties* fhese are reflected in electrical conduction mad dif«»

fusion which haw heen related in the Herat-Einstein equation.

Data are available at present for many pur© melts and binary

systems. However, it has heen found in almost all oases that

the self-diffusion coefficients of ionic melts do not correlate

satisfactorily with conductivity data. Since the Nerat-Einstein

equation was derived for dilute ionio solutions, it has heen

proposed that diffusion In ionio melts proceeds hy both single

ion and ion-pair mechanisms (11# 12). fhe latter mechanism

contributes only to the diffusion, thus* diffusional measure-

ment likely will fife more information than electrical con-

ductivity about the transport properties of the ionio melts.

In self•diffusion, there is no concentration gradient

©f opponents through the medium. Hence» measurements must he

carried out in the presence of traoer amount of isotopes of

the ions being investigated. At present, the isotopes used

are mostly restricted to those radioactive species that have

half-lives which are appreciably longer than the diffusion

experiments, fhe standard deviation of the measurements are

always about ten per cent. Nevertheless, considerable infor-

mation has been obtained by several experimental variations.

fhe method aost frequently used in capillary diffusion

(29) whioh will be described in detail In the next chapter#

4

Bookrls and Hooper (6) have reported measurements in which the

active isotope m a allowed t% diffuse from the bath into the

capillary in reverse t# the ueual direction* In these experi-

meat® a a§ effect correction has been affiled by several in-

vestigators (?, 11, 25, 31). lagara^an et al. (25) have com-

pared the activation energy of sodium ion in molten sodium

nitrate (4*5 Kcal/mole) to that obtained by the former method

(4*97 Kcal/mole} (32), When the aH effeet correction was ap-

plied to the molten sodium chloride, m decrease of about thir-

teen per cent in the activation energy was observed (6# 7).

Other investigators feel that such correction is not required

if a suitable stirring rate ia maintained during the diffusion

(6, 32). Talues for the diffusion coefficient have been shown

to be independent of stirring **te over a considerable range

when the active material is located either in or out of the

capillary (7» 23). However, the effect of thecorrection

seems to be much more important in the experiments where dif-

fusion of the tracer is from the bath into the capillary. A

possible explanation could be that concentration of radio-

active isotope at the mouth of the capillary is hi^ier in this

case than when diffusion occur® in the other direction.

Other techniques employed included the diffuaion-oouple

method (9, 37) and diaphragm diffusion (14). for the diffuaion-

oouple method, contact between the active and inactive regions is

made inside of the capillary which is sectioned before the freezing

of the melt. In a modification, suggested by L* S. Wallin,

the melt 1© allowed t@ freeze slowly before sectioning (33)*

for molten zinc bromide, a comparison of these date with thoee

previously obtained by capillary method (35) showed®. decrease

in the diffusion coefficient, While til© technique has the ad-

vantage of avoid the *1 effect, it i® necessary to compensate

for contraction of the melt during its freezing* Sjordjevlc

and Hill© (14) used the porous diaphragm to contain the active

»elt in studying the diffusion in molten sodium carbonate# fhe

effective diffusion length of the diaphragm m& obtained by

repeating measurements on molten sodium nitrate for calibration

purposes* fhe data from this method show a great deal of scatter.

fhe first published work ©f self-diffusion measurement

on molten salts me that of Berne and Kleiam (2) in whioh the

diffusion coefficient of thallium (X) ion is solten thallium

chloride was determined as a function of temperature ever the

range 487O0~5?7°C. fhe first published paper in whioh diffusion

was determined for both the cation and the anion was that of

fan Artsdalen and coworkers on sodium nitrate (32). A quite

complete table listing the work already done on various systems

iss available at present (19# 30)#

For molten alkali halides, complete ionization has been S

postulated from electrical conductivity data (8) and the hole

model has yielded satisfactory interpretation ©f the experi-

mental data (4)* For molten divalent aetal halides, complex-ion

formation or even some indication of polymorphism has been

6

suggtsitd{8}f Accordingly, the number of pbc1* Ions in molten

lead chloride was assumed to be such larger than that of i>b++

ions(8) * However, complete Ionization of molten lead chloride

ha® also been interpreted fmm Raman spectroscopic data(4).

In the case of sine halides, polymorphism has been suggested

(8). This might "be an explanation of the abnormally large ac-

tivation energy for zinc ion in aolten zinc bromide(34, 35) •

The study of binary molten salts systems began in this

X&baratory^S )* It was found that the diffusion of lead was

particularly hindered at the composition 2j>bC3a,lGl and that

Above 550°c# this anomalous behavior vanishes. This .suggests

the formation of some complex species in the mixtu$*©(S8) *

The saae behavior and conclusion were observed at J&Q mole$

XC1 in molten Nal-ECl mixture(31). In these two cases, the

electrical conductivity, vlseoeity, surface tension* and other

measurements agree with such postulation(5, 10, 17). other

binary systems have been studied toy Eookris, xoshHsawa, and

Richards(7), hut only the data for t >e diffusion of trace '

alltall metal chlorides in Hacl were obtained» Activation

energy was found to be dependent on the ionic radii of the

alkali metal Ions*

The PbcI2~Ma01 study . was begun in this laboratory by

wiraberley(34) who measured the self~diffusion of lead and

chloride ions. This was followed by Yin(38) and Lu(21) for

the self-diffusion of sodium ion in the same system* Lu noticed

that at a composition of ten per cent Nacl, there was a

f

considerable a m o u n t of N&-22 d i f f u s e d I n t o the P y r e x capll-

l & r i e f t u m A l a t h e p r e v i o u s m m u r e m m t m . f h l s activity ©an

so t be extracted by the w a t e r into the f i n a l counting solut ion

( s e e n e x t c h a p t e r ) * Therefore, t b e d i f f u s i o n r a t e s thu® ®fc*

t a i n e d w e r e h i g h e r t han , they s h o u l d have 1st e n * lu a lso observed

th&t t h e d i f f u s i o n c o e f f i c i e n t s o f Na*-22 "began to drop dras-

t i c a l l y a t t h e t e m p e r a t u r e s h i g h e r t h a n 540°c when pyrex

c a p i l l a r l e e w e r e e m p l o y e d .

v»hen q u a r t s c a p i l l a r i e s w e r e u s e d hy Lu t o measure the

d i f f u s i o n o f N&-22 a t e o i a p o s i t l o n o f 4*4? a n d 10#22 m o l e p e r

c e n t # t h e a c t t v & t i o a e n e r g i e s of sodium d i f f e r e d f o r t h e t w o

compositions* and v a r i e d from t h e v a l u e s reported by Yin. It

was* t h e r e f o r e * apt to c h e c k t h e d i f f u s i o n d a t a o f t o d i u ® over

a a e n t i r e r a n g e o f compositions t h a t t h e experiments d e s c r i b e d

1ft Chapter-II were performed.

o m m m bibliography

1, Bernal, J. , "la Attempt at a Molecular "Theory of Liquid Structure," transactions of the ffaraday Society. XXXIXI i, 1937) f 27 • _

2. Berne, S, a ad A# Klenm, »Se If iffusion of fhslliw* in lol«* ten thallium (I) Chloride," Zeitaofcrift fur faturftr** aohunjf* 8B (luly, 1953), 400. . ~ "

3# Bloagrem, G« B.» "Partition function for Noraal Liquida and Molten Salts," Annals ®f the Sew fork Academy of Sciences, M X U (Jaxaiary, 1^6077 751. '

4# Bloom, H- and J. 0*M« Bockris, "Structure Asjwtote of ionio liquids,« fused Salts, edited hy B. R. Sundheia, Hew York, McGraw-Hill, tnc., 1^64*

5# Bloom, H. and others, "Electrical Conduotivities, Activation Energies of Ionic Migration and Molar Tolumes of Molten Binary Halides Mixtures (I)," graneaotioieof the Faraday Society« XUX (1953), 1458.

6# Bockris, G*M« and §* W* Hooper* MS©If-diffusion in

XHXIE(196l" m " " 3 * " ^ R > r a a a y soeie-tr.

7. Bockris, J, 0*1., S. Xoshikawa and S. R. Richards, "Dif-fusion of Unlike Ions into Liquid Sodium Chloride," Journal of B&ysical Chemistry, XXTXXX (July, 1964), 1838.

8. Bockris, J. 0*M. and others, "the Electric Conductance of Simple Molten Blectolytes,« Proceedings of the Royal Sooiety. A255 (Bay, 196Q), 5551 ' —

9. Bockris^ and C. A. Angell,. Electroohim Acta, I

10. Bosrinsn, S, I#, A. R# Palmer and I. Beymnnp «2he Con-stitution of Ionic liquids. Mr* 3#* fraasaotiowof the

Society, II |1955), 277* . "" "

11* Boruote, &* 0«M» Bookria and J. A* Site toner, "Self-diffusion in Molten Sodiusi ChlorideProceedings of the Royal Society, A241 (September, 1957),

8

12, £aruGlBft# A* Z., J# 0*M« Boclo?is and J# A. Kitchener, «S$st of the Applicability of the fferst«43iaatei» Equation to Salf-4iffussi0n and Conduction of Ions is Molten Sodium Chloride," Journal of Chemical Physic®, XXI? (June, 1956), 12827"" * •

Carlson, C. IS., H. Eyring and f. He©, «Significant Structures in Liquids, II,« Proceedings of the National Academy of Science. XLVI (itorch, 1$W)9 TO" "**

13,

14* D^ord^eric, J. and G. J. Hills t * Ionic Self-diffusion Co-efficients in Molten Sodium Carbonate ,tt transactions of the Faraday Society, LVI (i960), 269. ' ~~

15* Eyring, E., 5. Ree and I, Hirai, "Significant Struotures in the liquid State, I," Proceedings of the " *""" 21 Science> XLIV (July7i$58), 6S57

16# Green, H# S., nip|it, Structure of Liquids ,* Bncyclopedia of Physics, Vol. X, Berlin, Julius Sfringer»'If""4"

17. Harrap* B. S* and E. Heyaann, »$he Constitution of Ionic Liquids, Part II,« transactions of the Faraday Society, LI (1955), 268. A

18. Kirksrcod, L. G., "Critic® of the Free Volume fheory of the Liquid State »n Journal of Chemical Physics * XVIII (larch, 1950), 580.

IS. Klemm, A., «fransport Properties of Molten Salts,* Molten §*££ 0hQ5^gky» e d i t?L! y M' B l a n d # r* s® w York» . S W T science Publishers, 1964.

20. Lennard-Jonea, $* s« and A. P. Devonshire, "Critioal Phenomena in the Gases I," Proceedings of the Royal Society, A163 (January,. 193?), 5 % -* ~

21. Lu, C. C., «Sodium Ion Self-diffusion in Molten Mixtures," unpublished master*s thesis, Department of Chemistry, , North fexas Stat® University, Denton, f#a»sg 1963.

22. Lunden, A., "Self-diffusion and the Structure of Molten Salts,» transaction Of Chalmers University of technology« lumber 241, Gotlienberg, Sweden,

25* Mills, R., WA Bemeasurame&t of the Self-41#fusion So-* efficients of Sodium Ion in Aqueous Sodium Chloride Solutions," Journal of American Chemical Society* LXXVII ( 1 9 5 5 ) — — "**

10

24# Moore, w*. J., Physical Chemistry, 3rd @<1., lagtXwsod ;uii? * w • %i * $ g g j ^ . . y T T si, * -/x u **Ur# $ Mii&vs Cliffs, lew $ersey,Iirtr@ri^i©#-«11, Inc. , l$6$

25* lagarajan. M. Kv, L. Mania and J* 0*1, Bookris, "Diffusion of Ha-22 in Molten Sodium Hitrate at Constant Volume," rournal of Physical Cheaistry, IXfXJt (September, 19643.

26, tfanis, 3>« and J. 0*1, Brockris, "Self-diffusion.- Heat of Activation as a function of Melting Temperature," Jourml of Physioal Chemistry, XXVII (December, 19*3), 2865":— —

27. Peek, H. X« a M ! , &• Hill, »0n theory of th# Liquid State," Journal of Physical Chemistry, XVIII (September, 1950), 1252:

28* Perkins, G. and others, wfh® Diffusion Coefficients of the Pb-210 and Cl-36 in Molten PbOlo-KOZ," Journal of ' Chemistry, MI? (December, I960), 1911«

29. Sad&injrton, K. and J. S. Anderson, "Tim Capillary Method for Determining Diffusion Coefficients," Journal of Chemical Society (1949), S381. ~~

30. Sundheim, B. R., "transport Properties of Liquid Bleetrolyt©s,tt fused Salts, edited by B* 1. Sundheim, Hew York* Hc&raw-SHX7 13577 1964.

31. OJricklebaok, S. 33., L. Hanis and J. 0*1* Bookris, "Diffusion In the System of Molten Sodium Iodide-Potassium Chloride," Journal of Playsical Chemistry, HCVIXJ (January, 1964}, 58.

32• Tan Artsdalen, E. R. and others, «Self-diffusion in Molten Sodium titrate,** Journal of the American Chemical Society. LXXVIII (lay, 1956) , 1772. ' "

33. Wallin, L. E., «Self-diffusion Measurements in Molten Salts,". 2-gitsehrifft fur laturforschung» 17® (February,,

34. . "Zinc Ion Self-diffusion in Htolten ginp Bromide," eitschrift fur laturforsehung, 17a (February, 1962), 195: .

35. Wallin, I*. I# and A* Lunden, "Self-diffusion of %im in Molten Zinc BromideZeitschrift fur Katurf orschun#?, 14a (March, 1953), 262. ' —

XI

36* Vamberley, J. W.# "Diffusion of Pb-210 an# 01-36 In the Molten PbCl2-HaCl System," unpublished ©astern thesis, Department of Chemistry, forth Texas State UiiiTersity,

19&Q*

37-* Yang, 1. and M, f * Simnal, Physicochemioa 1 leasureaentg , at gajfli temperatures< editea JJUylu#* b*Mrr'B6djd a «•» Eon&on, Butterwortha, 1959*

38'. Tin, H« S. 1*,: *Diffusion ©f la-22 is the Molten FbCl2» IctCl System" unpublished ussier*a thesis« Department

Chemistry, forth Texas Stat® University, of fsxas, 1962.

CHAPTER II

EXPERIMENTAL PROCEDURE AND RESULTS

Aa Investigation has been sad® of ttot penetrating dtptfc

and the relative amounts of Ma-22 diffusing into th® Pyrex,

Vyeor,and quartz rods# These were Immersed into Na-22 activated

tea aole per -mm.% Nad*Pbcl2 fixture for forty-eight hour®

at 530°C- They were removed, washed with water, and iieaaured

with a micrometer to determine their diameters*

The relative amounts of Na-22 diffusing Into the rods

were obtained by measuring the activity with an end-window

type G. M« tube connected to a Balrd Atomic scaler, Model

123* Total activities were divided by each surface area in

order to place the data on a comparable basis# For the pene-

tration determinations, these j*ods were placed In a tumbling

action polishing machine with a sludge of water and carbo-

rundum • The decreases in diameters and activities were aeas»

ured occasionally* penetration depth was estimated as half

of the diameter decrease from ita initial value.

Another- set of Ma«22 diffused rode was Immersed into

the polishing medium for two months without tumbling. No

detestable amount of Na-22 diffused from the rods In this

period* The relativ# aaounts of Na«*22 diffused into thee# rods

are in th® ratio quartst Vyeor: Pyre-x Is 34? 6800# The

12

13

penetration of Na-22 into Pyrex w m 0.0179 centimeter for

seventy-*seven per cent of total amount of K&-22 diffused. For

Vycor, it was 0,0140 centimeter for seventy per cent of total

amount of Ba-22 diffused. Figure 1 shows the relations be- ,

tween penetration depth and per cent activity remaining in

Pyrex and Vyoor.

Self-diffusion coefficients of sodium in the various

compositions of HaCl~PbCl2 mixtures were obtained, in geneml,

by the same apparatus and process described by Lu (2). A ninor

change was made in the procedure of activating the sample.

In these experiments the Ha-22 solution was transferred into

a Vyoor tube and heated to 'dryness, the sample to be activated

was added and leapt molten overnight to ensure thorough aiding.

Air was excluded in this heating process by first evacuating

the tube and then filling with argon*

Data were obtained as a function of temperature in the -

range 500~580°C and for the compositions 5.5* 10.0, 20.0, 30*0

and 45*0 mole per cent of sodium chloride• After plotting log D

as a function of l/P* in molten HaCl-PbClg mixtures, the best

straight line v/as calculated for each composition by an 3®*,

1620 computer program, for least square method. Equations of

the Arrhenius form, D=A exp (-AB/K)» were obtained in

which *2>tt is the* self-diffusion coefficient § BAM Is a constant %

"T" is the absolute temperature) HE* is the activation energy;

and wtf is the gas constant# fhe self "-diffusion coefficients

m

C/CL

1.0

0.8

0.6

0*4

0.2

* Vyoor

^ |»yr®x

0.4 0*8 1.2 1.6

D©pfch of P®netration, IO^cb

2.0

Fig. 1—Graph showing the depth of penetration of Ha-22 In Pyrex and Vyoor.

w

for mmh oapillary at varioua diffusion temperatures arid, com-

position* m well aa the best straight-line equations are

tabulated la fables I through V* Figures 2 through 6 a how

log D vereus 1/T tor the various compositions. Points are the

averag© of experimental values for the capillaries with the

probabl# deviations. 'I'iie line® ware drawn from the be it Ito©

equations. These are leparste# on a simple graph In Figurt

7 * fable VI tabulates thrii "best straIght-1 In© equations of the

various compositions investigated# For comparisons, pure

• sodium chloride (X) h&s beer* included- in Table VII th® best

straight-lines for lead and. chloride ions obtained by re-

calculating %h& data of Wi*!*rl«y(5) h&Y# been included* fUese

data will toe referred to in the discussion.

u

TABLE I

DNaX105 Gia2/sec ill FbCl2-5*5 mole% UaGl

0 T E Gap. I cup.XI C a p . I l l Cap.IY Average

789 s/( «*#**«*«• 2.34 2.29 1.98 2.21+0.15

811 sa 1.86 2.16 1.84 «wp m m «* 1.95±0.14

811 1.80 2.64 2 .38 2.02 2.21+0.30

8 1 5 ^ 1 .91 1.97 2 • 16 1.97 2•01+0.08

BJQss'/ 2.40 2 .61 2 .81 2 • 82 2.66+0.16

8 4 3 ^ 2*J2 2.76 3 .10 3.03 2.90±0.16

853 2.89 3*07 2 .77 2.69 2.86+0.12

r j J •>$/

T

/22, 7

For this compositions

D N a ( l ad . ) = 4.630X10 -3 exp(-8588ill25/RT3

Dg^Cavg.)= 3.296X10~5 exp(-80e9±l875/RT)

TABLE II

D^n*lo5 cm2/eec in pbC^-lO.O mole% NaCl

IT

T % C a p . 1 G a p . I I C a p » t I I C a p . I f A Y W & g ®

/ 2$, P$L 7 8 1 ' 2 . 3 6 2 . 2 9 2 , 1 0 2 . 2 6 2 . 2 5 ± 0 . 0 7

7 9 9 ^ r 2 # 1 5 2 , 1 6 2 * 1 7 2 . 2 2 2 . 1 7 ^ 0 . 0 3

*ZtJ e a i j v ,

V

IO

# VJ4

-*3

2 . 3 7 2 * 4 6 2 * 4 9 2 , 4 2 i 0 . 0 5

8 3 3 3 3 . 3 1 2 * 7 4 3 . 1 0 3 * 0 8 3 . 0 3 ± 0 . 1 5

//i, 2 . 8 4 6 ^ 7 j 3 * 0 7 3 * 3 2 3 . 0 9 3*20 3 . 1 7 ± 0 . 0 9

F o r t h i s c o m p o a i t i o n t

{ i n d *)~3 • 240XI ( T 3 e x p ( ~ ? 8 2 5 ± T 4 0 / R f }

% a (airg.)« 3«136 xiG^0xp{~7?7Q±156Q/HT)

13

TABLE III

1)^X105 cm2/®®® i n pbcX2"22.0 mol»$ NaCl

/2<

f °K Cap* 1 Cap#XX C&p*III Gap. IV Average

2 >28 2,30 2 *29 2.33 2.3010,02

807/:^ 2.45 2 <46 2.52 <«* # * * * «*K 2.4810.03

818..# jf"* mm 2.43 2*73 2•56+0.16

826 JT / 3.02 3*09 3-19 3*12 3.1010.05

854 si / 3.38 * » » - — 3.30 3.40 3,36±0.04

For thla compositiont

^ {ind • }= 3.03 Xicr3exp( ~7620±543/RT 5

Djja(avg. ) = 3»03xlO^xpf~7640tl 110/RT)

1 9

fABLE XV

DJIaX105 m % / m ® i n PbC 1 2 - 3 0 * 0 rao le^ N a C l

/2 /, U

T °K Gap* X C a p . I I C a p . I l l Cap* XV . A v e r a g e

7 8 8 -7 r 2 . 5 1 2 . 4 7 2 * 4 0 mm* mum 2 . 4 6 ± 0 , 0 4

8 0 3 J7 i? 2 . 6 3 2 . 4 1 2 * 9 4 2 . 9 0 2 . 7 2 + 0 . 2 0

8 2 0 ^ ? 2 *93 2 . 9 6 3 * 0 6 3 . 0 3 2 . 9 9 ± 0 , G 5

827Sf f 3 * 1 5 3 * 1 1 3 . 2 0 3 * 2 1 3 . 1 7 ± 0 . 0 4

8 5 1 J? :• 3 * h 3 #56 3 . 4 8 3 #-49 4 0 . 0 5

F o r t h i s c o m p o s i t i o n t

% & ( l a d . ) = 3 * 0 9 l G M \ x p ( - 7 5 5 0 ± 4 ? 2 / r t )

% a ( a T g . , ) = 2 . 9 7 l c r 3 e X p ( - 7 4 9 0 i 2 5 4 / H T )

TABLE ¥

DnaXl# in Ptoo12*45»0 mol®% NaCl

20

T °ll

'HM 806 J?,f 3*18

'*/•*? 826 j j

"f-ti m j z

HIM" i'i

Gap. I

t 3.31

5 *87

Cap.II

2.83

3.29

3*72

3.82

Cap.Ill

2*99

3*40

3.48

cap.rv

3.60

,47

3*98

Average

3*00+0.12

3«43±0,11

3.49i0.ll"

3.89±0.06

f- For $bli composition:

fi^A(lnd.) ~2.8!X10*5exp(.7260+625/RT )

% a (&*6 •) =» 2.58X!0"3«xp {-7140+702/rt }

21

TABLE VI

S^raigbt*lla® Equations for tbe Various composition® of M&

Composition %&» cm2/®®® mole $ %&» cm2/®®®

5*5 4,63 X 10-3 exp(«8588±X125/RT)

10*0 3.24 X 10"5 exp{-?825±?40/et)

22 #0 3»03 X10"3 exp(-7620 + 543/RT)

30*0 3 • 09 x 10-5 | x p (^ 5 5o + 4?2/Rf}

45*0 2.81X 10"5 exp(-7620± 625/RT)

•twr® nmi 1,49XlO"5 exp(-6800 ± 500/rt)

*Boo&rl» and Hooper(1)

22

TABLE VII

Straight-lin« Equations for the Various Compositions 9t FbClg*

0 oupos 111011 SAL® % Dpk» cm2/0© o X>Q1» m2/m<&

fur® PBCLG 7.56XlCT4exp(-6745/RT) 8.83^10-4exp(-6068/RT)

AGAO 9 *15 Xio'^exp(-6704/RT) 13.4XIO"4txp(-6544/RT )

72*98 13.90 xi Cf *exp(-7344/RT) 16.8xiQ~4exp(HS844/R'f)

65.06 12«90XL0^exp(-7053/RT) 13 •LXIO*"4«xp( -6308/RT )

52*49 18.10X10~4exp( -7424/RT ) 2 5.4 10"4« xp(-7340/RT)

•Wimfoerley's dat*(3) after recalculation

23

6

5

4

U q)

*"• o

•iv...

1#16 1.18 1.20 1 «22 1*24 1*26 1.28

1000 1/T,

Pig. 2—araph ®howl*ig variation of log B with 1/f for the Bf&%m PbCl2-5*5aole % sioiJ

24

0

§ 3

\ *

Q

1.17 1.19 1.21 1.23 1.25

1000 1/T, °K

1.27 1*29

Fig. 3—Graph showing variation of log D a v g. with l/f

for %tm ay&%m pbolg-10 aol®$ MaCl*

25

si

i V) '

% 2

T

1*16 1.18 1.20 1.22 1.24

1000 1A» °K

1.26 1.28

Fig. 4—ftrapii showing variation of log D a V g. with l/T

for lim system FbClg-22.0 saol©$ H&Cl*

26

V 3 y

V \

*

«0 2

cf

1.16 1.18 1.20 1.22 1.24 1.26 1.23

1000 1/T, °S

Fig* 5--©rapfct showing variation of log D a v g # with 1/T for tlie system Pfcelg-SO.O is©1®$ H&Cl.

27

6

5

4

J V* 3

\ §?

1*14 1.16 1.18 1.20 1.22 1.24

1000 l/r» %

1.26

Fig* 6—tr&ph shewing variation of log Bavg# with 1/p for %im system l»kClg-45»0 ia®l@$ n®01.

26

0

V <o %

\ 2

3

lli. 1.16 1.18 1*20 1.22 1.24

1000 1/T, \

1.26 1.28

Fig. 7—(Jraph showing variation at log D^ad# with l/f

for various eorapesltlous of Had ln'ybc^.

CHilPTEH BIBilOGIUPHy

1. ''flfeokrls, J. 0»M. and G. W. Hooter, "Self-diffusion Is 'Molten Altali Hal ides," Plseussions of the ~ ' • *, ran (1961), 218, -

2* !«*, 0* C., "Sodium Ion Self-dif fusion in Molten Mixtures," unpublished mater's tresis, Department of Chemistry, Morth fern® Stat® University, Donton, f exas, 1963.

3* Wimfcerloy, J. w«f "Diffusion of Pb-310 and 01-56 in the Molten PbGl2-HaCl Systea," unpublished master*s thesis, Department of Chemistry, forth fexaa Stat# University, Denton, Texas, I960.

29

CHAPTER III

DISCUSSION

fhe data obtained from the diffusion ©f Na-22 into the

glass rods are in agreestnt with what was to be expected. Ttae

relative amounts of Ma-22 diffused increased for the higher

aodium content glasses. The depths of penetration for pyrex

and Vycor are about the same and are quit# comparable with

that observed for soda-lime glass by R. H. Dorenm© (10). a®

observed that ninety ~per cent of Ha-22 aotivity was within

200 microns * However, the diffusion temperature employed by

Doreaaue was only 374° C» diffusion tlsae was nineteen how®, and

the activation energy was estimated as twenty Koal/stole« Thus,

the diffusion rata should increase rapidly at higher temper-

atures. H® appreciable Mount of la-22 diffused into quart®

under conditions investigated. later, when higher diffusion

temperatures near 58CPc were employed, a email but insignif-

icant amount of activity wae detected in th® washed quarta

powders.

The diffusion coefficients measured in these experiment-©

are smaller at the lower teaperature and larger at the higher

temperatures than corresponding data obtained by Xln(2?)»

This increases the activation energies by about 3*5 Kcal/aiole.

Tfee large deviation found by Im(17) between 4.4? mole per cent

and 10.22 mole per cent of sodium chloride was not found in

30

31

these measurements. At intermediate temperatures, all of th©

data are is fair agreement. At the compositions 5.5 mole per |

mntf 10*0 mole per cent# and 22.0 mole per ©eat of sodium

chloride there 1» a suggestion of a more rapid increase ia

diffusion coefficients at about 550°C• Howler, the points

still are ia satisfactory agreement with the calculated fc@st

Hmm* I

Tan Artsdalen and Yaffe (24) have explained the deviation

from additive behavior of the equivalent conductance ia molten

salts as resulting from the replacement of ions in the fwasi*

semi-lattices of the pure salts by those of the other salts

present in the mixture. In the case of large deviation from

additivity, mmb a® in the KOl-FbGlg system, the eseistonce

of complex-ion® has been postulated (5)* Various methods have

been used to provide evidence of ooaplox-ion formation ia

binary mixtures* These have been listed by H. Bloom (4)* In

the particular systems of alkali chlorides with lead chloride

the deviations from additlvity for equivalent conductance and

molar volume measurement® have been found to increase as does

the size of the alkali metal cation. Accordingly, this has

been interpreted as the result of the increased importance

of complex-ion formation. Since the deviations for the faCl-

3?b0l2 system are unexceptlonally small for the equivalent c@n»

ductance, molar volume (4) and surface tension (2)# the pos-

sibility of complex-ion formation in this system is in doubt*

32

Tarlation of the activation energy of self-diffusion in

the KCl-PbCl2 system has been attributed to complex-ion formation.

While variation is evident in the HaCl-PtClg system, it is not

as marked as reported in the JC01-F&C12 system (.20)# figure 8

gives this variation as a function of concentration.

fhe activation energy for sodium decreases at higher oon-

centrations. for "both Pb* and 01% increases i n noted# fhis

oeuld be interpreted as supporting to the suggestion of Van

Artsdalen and Yaffe. However, the variation in experimental

value® is so large as to leave a question as to its validity#

fhe appearance of peaks in the vicinity of thirty per cent

sodium chloride for lead and chloride ions could be explained

in terns of complex-ion formation similar to the case of 101-

PbCl2 system, fh® degree of complex-ion formation must he

much smaller than that of the EPl-PbGXg system, fhis would

agree with Bloom's observations of smaller deviations from

additivity of equivalent conductance and molar volume meas^

urements in the Sa01-PhCl2 system# fhe maximum activation

energy in the vicinity of thirty mole per cent sodium chloride

is consistent with other measurements made with this system*

the freezing point (22) and surface tension (2) show minimum

values at this composition while there Is a maximum deviation

from additivity for equivalent conductance and molar volume (4).

Another significant observation from the above plot is

that the activation energies of the three components inves-

tigated are likely to Tm equal near fifty mole per' cent

33

I

<*

$ *

* eodium Ion

9000 . * lead Ion

• chloride ion

8000 .

7000 .

X

, I|#

i / / / / / / / / / / _4

6000

m

6000

# • t • .

20 40 60

Molt % KaCl

80 100

Fig« 8—Graph showing the activation energies of sodium, lead, and c hi orid© ions as a function of composition of M a d in laolteri S&Cl-PlJClg mixture.

34

composition* This would suggest that all three components in

the. mixture behave alike at this composition# Other consider-

ations lead to the suggestion that "complete ionization" ©o-

curs at this composition*

It fables VHI* IX, and X show the diffusion isothtwa

of sodium, lead, and chloride ions which are calculated froit

the bmi straight-line equations of these components* $h®y

mm plotted in figures 9 and 10. The diffusion coefficients

are found to increase linearly with the increase of sodium

chloride concentration, fhs ©light &mrmm in diffusion at

thirty mole per cent sodium chloride could indicate some com-

plex-don formation. If the values of pure sodium chloride are

given consideration* a mximm diffusion coefficient is noted

at fifty mole per cent composition. I&ter, it can he shown

that the ratio of diffusion coefficients of lead and chloride

ions or sodiua and chloride ion# art consistent with those of

complete ionized molten salts. \

2. Bloom (4) found that the specific conductance of NaCl

PhCl2 showed linear increase over a teaperature interval of

more than 150^0 beginning just above the melting point. This

is what would be expected for a non-complex-ion species.

3. Bootois and Angell (7) measured the diffusion coef-

ficients of oadiiiua ion in ECl-OdOlg mixture at 470°0. A max-

ima, has also been found at th« fifty mole per cent KC1 op-

position*' fheir conclusion was that cadmium chloride contains

TABLE VIII

Diffusion Isotherms of Sodium

35

Composition mole % 500°c 550°0 600°0

5-5 i.74^10"5 2*41x10-5 3.27X10*5

10.0 1.98XI0""5 2.71X10*5 3.57x10-5

22.0 2.11X10-5 2.86X10"5 3.76X10-5

30.0 2 •26x10"-' 3.06X10*5 4.00X10"5

45*0 2.49X10*"5 3.32x10"" 5 4.29X10-5

Fur# NaCl« 1.78x10*5 2.33X10"5 2.98X10-5

•Bockrle and Hooper(8)

TABLE IX

Dif fus ion I®othe ma of L©a&

36

Composition mole % 500°0 550°0 6OO0G

pure PbCla o,95*io~5 1.22U0" 5 1.54X10"5

82.10 1.16X10"5 1.53X10"5 1.93X10*5

72,98 1.16/10"5 1.56 *10" 5 2.02X10"5

63*06 1.30XXO"5 1-73UO"*5 2.23X10"5

52.49 1.44 xio"5 1.93X10-5 2.51X10-5

TABLE X

Diffusion isotherms of cftlorid*

37

Composition mols % 5O0®c 550°C 600°C

Fur© pbClg X.68X10"5 2 • 15*10""'"* 2.67*10"5

82.10 1.88*10"5 2.45^10*5 3.08X10*5

72. as 1« 94x10"" 5 2.55*10"5 3.23X10"5

65«QS 2.15 MO"5 2.77XI0"5 3.45*10"5

52.49 2.12X1Q"5 2.85X10"^ 3.69X10"^

u ty

5 o \ X

4 . 6 .

3 *8 •

3 . 0

Q 2 .2

1*4

38

10 20 30

Hoi* % MaCl

Fig* 9—Dif fus ion iigtlierffls of sodluii Ion a t 500 ° c , 550 o» and 600 ° o .

\ 2«8 «

60 70 80

m&u % wmx2

90 100

P i g . lO—Diffuaion IsotherauB of l e s t and oh le r id* Una a t 500°c, 550°C, and 600°c.

39

associated species which break down increasingly upon addition

of potassium chloride»

laity (15) suggested that negative values for the like-

ion friction o©efficient can be criterion for the presence

of association in the species, flatus§ lie Stowed that there la

definite evidence of association in molten alno bromide,

wlille that In thallium (I) chloride is uncertain (16). Using

tills criterion | Yin showed association to be present la molten

load chloride (26)» It would "be interesting to show that this

criterion supports the suggestion of non-association in

molten laCl-FbClg mixture* However, this can he done only

after the data for inter-diffusion of lead and sodium ions

have been obtained. Such data are lacking at the present.

However, the observation of "complete ionization" at fifty

mole per cent sodium chloride will not reveal structural de-

tails ©f the liquid melts» Since short-range order ha® been

found in pure molten salts near the melting point, the same

situation is likely to prevail in mixtures. The addition of

small amounts of second material would allow two separate

§uasi-semi-la ttice types to exist in the liquid mixture as

was suggested by Tan Artsdalen and Taffe« The clusters of the

minor component would be surrounded by those of the major

salt. As a consequence, there would be available sufficient

amounts of the major component to produce distortion in all

clusters of tile minor component. && the composition approaches

40

fifty mole perocent value, neither would remain as the pre-

dominant species and the structure, as a whole, could be con-

sidered *8 a distinct species. f3» mixture, as a whole, could

be taken as a newly "formed" lattice in which interactions

will be at minimum, fhis can explain the maximum in diffusion

coefficient and the equal activation energy observed for all

three component© in the mixture laGl-PbClg, since this "lattice"

would be characterized by its own melting temperature. Bookria

@t al. (8, 18), have reported that activation energies for

diffusion are dependent upon the melting temperature.

Bloom and Hermann (5) observed a minimum in electrical

conductance for KCl- PbCl2 and KCl~CdCl2 mixtures at fifty ®ole

per cent KC1 even at the temperature of 720°C. Sfcsy «sata»d

"stable compounds« had been formed at this composition in

both cases. fhe term "complex-ion" has meaning only in a

statistical sense* If the life-time of the unit is much

larger than the average collision interval, it could be main-

tained that the speoies is an independent unit. Even in the

case v#f assumed complete ionization, short-range order is found

in the existence of ion clusters which undergo frequent ex-

change in their outer regions* Bloom and Bockria (6) enu-

merated four facts that can prove complex-ion formation and

showed that complex-ions (most likely CdClj"*) likely exist

in KCl-CdGlg mixture# - If this is true# this mixture can

b© considered to consist of CdC^** and K*" ions with a larger

41

" free volume" than that of either of the par® melts (13)* The

formation and dissociation of CdOlj" occur relatively faster

than the rate ©f diffusion, fills oould explain the maximum

diffusion coefficient of this composition (7)» tfhua, "complete

ionization* ©an he thought as a specific case in which the

complex ions (possibly PbCij~) are so unstable that they have

no significant influence.

As mentioned earlier* the hole model gives considerable

success in estimating activation energies of diffusion for

molten salts (18)# No model has been successful in predicting

the diffusion coefficient (IB}* It has been found that in some

cases the ratio of diffusion coefficients for the two compo-

nents in pure molten salts can b® related to the rati# of ionic

radii of the components# In other cases, the ratio of masses

is more important. Since molten salts» near th«ir melting

point# are more "oryetal-lilceit would be interesting to

see whether there are some relations between the me It lag point

of the salts and diffusion coefficient of their components

at this temperature. Calculated values from the best straight-

line equations are listed in fable XI • figure 11 shows the

resulting plot# in the form of log D versus %» for various

systems that have been investigated, ?ery reasonable straight

lines can be drawn among chloride ions (except for thallium

chloride), nitrate ions and carbonate i®»f and for ssinc-lead-

cadmium ions* The alkali metal ions exhibit a greater scat-

tering. fhe exceptional case of molten thallium (I) chloride

$mm i i OAKHJUTED SE -DIPPUSIOH OOS3WIOIEBTS Of YAHIOUS

MQWm SAISIS AS TKB K » » POI®

42

Molten Salts Ions jw>">5

(cm /see) Melting feat *

®K t©f*

AglO Ag +

IO3-1.02 0.57

485 11 11

nUBOf~~ 103"* 0.47

—u 11 ' 11 Maffij

' '

Sa* HO3-

' 'i.fS — 1.09

m i — ™ II ™ 11

10 ~ i j i 1.17

ffif 11

CaNOj Cs+

1%"" 1.86 1.80

687 " 11 11

SnBri ' Si* 1 w 1 "Jl n * ""25* -IS8I2" •"••« ,lf|f¥-"J"l"J"

Cl~ &.§§• 1*70

"" 1$ — 19

4 * # f c - w ^L, "51*"' 01~

2.86" 2.22 703 f ' Il1""

14 Cd012 <nr

2.62 2*38

868* 1 1

CaCl ' Cs+"l'"'J1

01-'5.19 3-39

919 8 8 StJf " 1 lln"'ff*cl' 1

c r • 4 •28"

3.85 '""1UII"~"1" 988 - W

8 Hal "i£+

i"* 7.07 3*70

HI If ' 23 • feci Ia+

01" 8,40 5.92

' f

1077 8 8

'jRSjgCCK; CO3 27.90

" ,lil6'9^— 9

KOI o r 1*46 20 " fioio HaCI

is+

Ffo* 01"*

3.28 1.87 2.79

814 This Bipei 26 26

*Not the melting point.

0 <u *

s

X

of

4?

01" and I"

HOj"* And COj

Cd ,P"b ,zn

univalent cation

400 600 800

o fra# I

1000 1200

Fig. 11—self-dlffuaton coefficient of various ions at the melting point as a function of a®Itlug t©nip©ratur©•

44

could be due to i, higher degree of association betwefn thai*

Hum and chloride lons{l6)« Values at fifty raole per cent

are higher In both KCl~PbCl2 NaCl-PbClg systems and lower

in the Nal-KCl &yste«(f©r the sodium ion value). This supports

the view that sore association exists In the pure salts for

the first two cases and that the opposite is true for the last

cast. Thus, attempt® to correlate the diffusion coefficients

of the molten ©alts and their melting temperature® "by a slraple

equation have not been iuccessful$18).

Furukawa has reported on the importance of electronic

polarizability of the ions in relating th© volume change and

activation energy of electrical conductivity at the melting

temperature for molten alkali halides(12)• in an extension

of correlation to the ratio of diffusion coefficients of ion§

at the melting temperature. Figure 12 ha® been obtained# In

this figure electronic pojarizabllity difference between com-

ponent lone in the melt are plotted against x* X 1b expressed

In the form (D +AO T h i= where Is the ratio

of self-diffusion coefflc&entt of cation and anion at the

melting temperature, and (M-/M+) is the ratio of the ra&sees

of anion and cation* Table XIX lists the corresponding value®.

Prom this plot the following relationships are to be

noted•

1* Ae the difference in electronic polsrlss&blllty between

the component ions decreases, the influence of mass on

45

TABLE XII

Electron!© p o l & r l z a b l l t t l e s and X f o r Cer ta in Molten s a l t s

Molten S a l t s

M-/1& + X A e<

C&NO3 1*032 • 0.468 -25 .70 0.02

C»C1 0*944 0.267 22.60 0.38

RbCl 1.110 0*417 «* 8 .40 0.98

CdClg 1.100 0.270 -13 .80 1.16

AgNOj 1.T77 0.575 - 0.96 1.53

T1C1 1.290 0.174 -•"6*92 1.84

FWlg 0.558 0.171 3 .03 1.94

I»03 1.128 1.585 3.82 2.48

KaCl 1.420 1.543 1.24 2.55

LINO3 2.845 8.930 2.09 3.37

Sa2C03 0.690 2.610 - 2 .58 3 .69

Hal 1.910 5.515 2.64 6.02

PbCl2 'KCl 0.692 (P15C lg )

0 .171 4 .80 1.94

PbClg*laCl 0.670 (PbClo) 1.176

(SaOl)

0.171

1.543

4.43

2 .68

1.94

2.52

(D+/B-}fm-(!-/&+} i A

Fig* 12—The dlfftreac# of •ltctronic polar-ltablllty for va-rious salts a® a function of x*

47

diffusion coefficient decreases.

2. Apparently, two curves can "be drawn in this plot.

The upper solid line coroeaponda to the equation (X-l.S)^ 4.1,

while the lower gdid line corresponds to (*»<«G»5) (X-3.0) = -4.1.

No explanation will 'be given in this paper for this particular

phenomenon* (1st® that a slight variation for the values of

diffusion coefficient or electronic polarizsbility in the region

4o«l will result in relatively large change of X. for example,

in the case of cesium nitrate, a six per cent decrease ia &if*»

fusion coefficient of cesium ion will isak© the change of X

from -25.7 to+ 25.%)

3. (D+/D-)$» of M l PbCl2 and HaCI PbCl2 mixtures fit

quit© well to the upper curve. If the calculation is made for

ths diffusing species as being PbCl+ and 01"% the value ob-

tained for X will not fit the curve.

4. The value of X for thallium chloride does not fit the

curves. So valid comparison can be made in the cases of »©*>

dim carbonate and cadmium chloride for which diffusions 1 data

were taken at only one temperature. However, the value for

cadmium chloride does seem reasonable.

5* Values of electronic polarizability used here are

those given by Tessiaan and Kahn (21) for crystals. While other -

scales are available, the observation that 33+/D- for solids

approach the same values observed in liquids at the melting

point (6) Justifies this choice of value® and support® the

lattice model.

4B

It is apparent that a great number of additional mate-

rial® should be investigated before there will be available

data sufficient to establish the behavior of molten systems.

Lack of information on lnter-dlffuslon coefficients prevent*

an investigation of the friction coefficients in salt mix-

tures. Self-diffusion studies on a larger number of non-as-

sociated materials having coiaaon ioniare needed. Only in ttoe

case of sodium compounds are data to be found for more ttian

one or two pure materials let alone for ionic mixturee. For

species containing association only cadmium chloride, thalllu®

chloride and zinc broolcle are available at this time. The

testing of the influence of electronic polarizability need®

values established for additional materials having differences

larger than four and smaller than on®. It is suggested that

the following species ©hould be considered by future inves-

tigators; lead bromide{<*<*=©.?4)» silver chloride{-*<< = 0.56)#

thallium carbonate(aoos1.1), and alkali(or alkali-earth)

§©l@nide{or telluride) ( cx.«4-8).

C M M M BIBLIOGRAPHY

1. Aagell, C, A. and J. W. Toaliason, "Self-diffusion and Electrical Conductance Measurement on Solution of Gad-mitt® in Molten ©admium Chloridet" Discussions of the Faraday Sooiety. tail (1961), § 3 7 7 — - — —

2* Baraakovskli, ?. P . , "She Density, Visooalty, Blectri© Conductivity and Surfaoe Tension of Seas Binary Salt Systems in the Fused State," Bulletin of the of Science of Russia (TOSS), 7" (1940'),""B257~

3. Berne, £» and A* Kl@m&t »Self~diffusion of fhallium in Molten Thallium (I) Chloride," Zeitschrift fur Hatur-forsohun&» 8a (July, 1953), 400.

4# Bloom, H., "Hecent Progress in the High temperature Chem-istry of Inorganic Salt System,1* the Official Journal of the International Union of Pure and Applied" Chemistry, tott9^), " m : — r — 1 — — 1 — —

5. Bloom, H. and B. Hsymann, "The Electric Conductivity and the Activation Energy of Ionic Migration of Molten Salts and fihelr Mixtures," Proceedings of the loyal Society, A188 (February, 194?),15§.

6. Bloom, H., and J. 0*M« Bookrie, "Structural Aspects of Ionic liquids,B Fused Salts, edited by B. B. Sundheisu lew York, McGraw-Sill, Inc., 1964*

7. Bookris, J. 0»M. and 0* A* Angell, Sleotroohis Acta. I (1959), 308. _ ~~

8. Bookris, J. 0»I. and G. f. Hooper, "Self-diffusion Co-officiants in Molten Alkali Halides*"' Discussions of the Faraday Society, XXXII (1961), 218. "~

9- Djord^evic, S. and G. J. Hills, "Ionic Self-diffusion Co-efficients in Molten Carbonate," transactions of the

Society, WX (I960), 267. ^ '

10. Doremus, E* H«, "Exchange and diffusion of Ions in Glass," Journal of Physical Chemistry» I»XVIII (August, 1964), 2212.

49

50

11. DwrorMin, A* S», R. B* Issue and B. 1* Tan Arisdalen, "Self-diffusion in Molten Nitrates," Journal of

'» ISJf (July, I960), 872.

12. Furukawa, K., "Structure of Molten Salts fear the Melting Point»*,Discussions of the ffaraday Society. XXXII (1961), 53 •

13# Barray, I. 3. and E. Heynann, «fh@ Constitution of Ionic Liquids, fart II,** Igraneactlona of the ffaraday Society* LI (1955), 268.

14. Klesna, A., "Transport Properties of Molten Salts," Melttn Salt Chemistry. edited by 1, Blander, lew York. Inter-science IhMishers, Inc., 1§64*

15# Laity, R. W.f "General Approach to the Study of Electrical Conductance and Ita [email protected] to teas fransport Phenomena Journal of Chemical Physics. XXX (March, 1959)» 682.

16. Laity, 1. W., "Interionic friction Coefficients in lolten Salts," Annals of the law fork Academy of Science, LXXIX (January, I960)~957T ^

17. Lu, C. C., "Sodium Ion Self-diffusion in Molten Mixtures," unpublished master*@ thesis. Department of Chemistry, fforth fexas State University, Denton, Texas, 1963.

18. lanis, L. and J. 0*M« Bockris, "Self-diffusion. Heat of Activation As a Function of Melting SDeajjjerature,« Journal of gterfcioal Chemistry. ISfll (December, 1963), 2865:

19. Perkins, and others, "Self-diffusion in Molten Pb0l2,» Journal of Physical Chemistry. LXIT (lortaber, I960), 1792.

20. Perkins, S. and other®, »$he Diffusion of Pb~210 and 01*36 in Molten PbCl2-KCl Mixtures in the Tioinity of the ' Composition 2PbCl2.KCl," Journal of Physical Chemistry, LXI? (December, I960), 1 9 m

21. Sessman, J. &• and A. H. Kahn, "Electronic Polarimbilitlea of Ions in Crystals,« Physical Beview. XOII (November* 1955), 690.

22.

Publishers, Inc., I960.

51

23* frieiaebaokp S. B., L. lanis and J, 0*1# Bockris, "Diffusion in the System Molten Sodium Iodide-Potassium Chloride Journal of Physical Chemistry. 1XVTII {January, 19645# 58.

24# Tan Arts&slen, S. H. and I. s. Xaffe, "Electrical Con-ductance and Density of Molten Salt Systems; KCl~LiCl, Kcl-IaCl and K01-KI." Journal of Physical Chemistry. M X (February, 1955), XSSI m **

25. Wallin, L. B. and A. Lunden, "Self-diffusion of Zinc in Molten' Zinc Bromide#

n Seitechrift fur la turforschun&# 14a Clttfftk, 1953), 262; **

26. Wimberley, J. W,t "Diffusion of Pb~210 and Cl-36 in the loltea PbCl2-HaCl System," unpublished master*s thesis, Department of Chemistry, forth fexas State University, Denton, Sexas, I960.

27. Tin, H. S. M., *»Diffusion of Sa«f2 in the Molten PhClg^ HaCI System," unpublished master's thesis, Department of Chemistry, forth fexas State University* Denton, $e»s, 1962.

BIBLIOGEAPHT

Books

Bloom, H. and 3» 0*M. Bookris, "Structure Aspects of lonio Liquids." fused Salts, edited fey B. H. Sundheim* lew York* w k m ^ m X T l n L , 19U*

Klenua, A., "transport Properties of Molten Salts.," Moltta Salt Cherniatry* edited by 1. Blander, lew fork, InterBcieace HBHilere, lm* f 1964.

Moor©, W* J., Phyaioal Chemistry, 3rd ed., Engelwood Cliffs, lew jer88y,Prenti09-Hall, Inc., 1962.

Sundheim, B. l.f "Transport Properties of liquid Electrolytes," Fused Salts*, edited lay B. H. Sundheim, few York# Mo®raw-ffitti; IS5T7 1964.

Sinuraanst J., fhe Physioo-chemical Con&tanta ©f Binary Systems in Concentrated solutions, iew York, interacience Publishers, Inc., 1 W . —

Yang, 1. and M. T« Stenal, Physieo~chemieaI Measurements at High Temperatures, edited by J* o»lt« Bookris it ai» Condon, ^uxterworths t' 19^9 •

Articles

Angell, C. A. and J. W. Uomlinaon, "Self-diffusion and Electrical Conductance Measurement on Solution of Cadmium in Molten Cadmium Chloride." Discussions of the faraday Society, XXXII (1961), 237. . '

Sarzakovskii, V, P», Mfhe Density, Viscosity, Electric Conduc-tivity and Surface tension of Some Binary Salt Systems in the fused State#

M Bulletin of the Academy of Science ©f Russia iSMi) t v (1W)» 8257 ' "" ' ~~"

Bernal, J. D., "An Attempt at a Molecular fheory of Liquid Structure," transaction® of Faraday Society*, XXXIII (1937)» 27#

52

53

B«rM, 1* and A. lies®, "Self-diffusion of Thallium in Molten . thallium (I) Chloride." Zeitschrift fur laturforsehung. 8R (July, 1955), 400#

Blomgrem, G. E., "Partition function for Normal Liquids and Molten Salts** Anna la of the lew York Academy of Sciences, T.YYTY (January, I960) ,"T8l^ ' **"" --------------^fi»PrPiwi m %r *ipHr ^jp » M0t *w $ 9 fp ^Nir #9*- ~

Bloom, H. , "Recent Progress in the High Temperature Chemistry of Inorganic Salt System," fhe Official Journal of the International Union of Pure and Applied Whealstry, til ( W 3 ) , 369. **

Bloom, H. and 1. Heymann, "The Bitotrio Conductivity and the Activation Energy of Ionic Migration of Molten Salts and Their Mixtures," Proceedings of the loyal Society* A188 (February, 1947),

Bloom H. and others, "Slectrical Conductivities, Activation .Energies of Ionic Migration and Molar Volumes of Molten Binary Glides Mixtures (I),'1 Iransactiomof the Faraday Society* XJJX (1953), 1458. ^

Bockris• J. 0*1. and C. A* An&ell. Uleotrochim Acta. I (1959). 308. ^

Bockris, J. 0*M» and 0. W. Hooper, wSelf-diffusion in Molten Alkali Halides," Discussions of the Faraday Society, XXIII (1961), 218. *

Bockris, J. 0*M., S. Toshikawa and S. 1. Richards, "Diffusion of Unlike Ions into Idauld Sodiun Chloride,« Journal of Physical Chemistry, OTI1I (July, 1964), 1838.

Bockris, J. 0»M. and others, "The Electric Conductance ©f Simple Molten Bleotolytes," Proceedings of the Royal Society, A255 (lay, I960), 558. * — * *~

Boardaan, H. .K., A. R. Palmer and I. Heymann, "The Constitution of Ionio Liquids. Part 3," transactions of the Faraday Society. II (1955), 277. ^

Borucka, A. Z., J. 0*M. Bockris and J. A. Kitchener, "fast of the Applicability of the Mernst-Einstein Equation to Self-diffusion and Conduction of Ions in Molten Sodium Chlordie," Journal of Chemical Physics. XXIV (June, 1956), 1282.

Borucka, A. Z., J. 0*M. Bockris and J. A. Kitchener, "Self-4iffusion in Molten Sodium Chloride," Proceeding of the Royal Society. A241 (September, 1957), 554.

54

Carlson. 0. M., H. Eyring and T. Ree, "Significant Structure* in Liquids, II," Proceedings of the national Academy of Scieacts, XLTI (March, 19&G)

D^ordjevio, S. and G. J. Hills, "Ionic Self-diffusion Coeffi-cients in Molten Sodium Carbonatef

w transactions of the Faraday Society. LYI (i960), 269.

l)oremus, B# H., "Exchange and Diffusion of Ions in Glass." Journal of Itersical Chemistry, EXTOI {August, 1964}, 2212.

Brorkin, A. S., R» B. Bsoue and £• fi. Yan Artsdalen, "Self-diffusion in Molten litrates," Journal of Physical Chemistry* LXIV (July, I960), 872.

Byring, B.f f. Bee and I« Hirai, "Significant Structures in the Liquid State, I," Proceedings of the gatioml Agad.fBI M Science. XLIY (July, 1958), 6857

Furukawa, &., «Structure of Molten Salts lear the Melting Point," Biacuaaio&s of the Faraday Society# XXXII (1961), 53.

Harra®, B. S* and 1* Heymann, "the Constitution of Ionic HqMtde, Part II," ffransactions of the faraday Society. LI (1955), 268.

Kiricwood, L. Q*, "Critique of the Free Volume theory of the Liquid State »* Journal of Chemical Physics. If III {March* 1950) # 380.

Journal of Chemical Physios. XXX (March, 1959), 682

Laity, B. W., "Interionic friction Coefficients in Molten Salts," Annals of the lew York Academy of Science, LXX1X (January. vswii'wn

Lennard-Jones, J. B. and A# f* Devonshire, "Critioal Phenomena in the 0asea I«w Proceedings of the loyal Society. A165 (January, 19375, 53. *

Lunden, A., "Self-diffusion and the Structure of Molten Baits," transactions of Chalmers University of Technology, lumber 241» §oihenberg, Sweden,11%1.

Mills, a., "A Kemeasurement of the Self-diffusion Coefficients of Sodium Ion in Aqueous Sodium Chloride Solutions,** Journal of American Chemical Society,. LXXfll (December. 1555), 6IT6:

55

Imgar&jan, J. K., I». faitis and J. 0»M* Sookris, "Diffusion • of Ma-22 in Molten Sodium litrate at Constant VolumeJournal of Physical Chemistry> LXVIII (September* 1964), 2726*

Kanls, L* and J. 0*M. Bockris, "Self-diffusion. Heat of Activation as a function of Melting TemperatureJournal of Physical Chemistry, XXYII (December, 1963), 2865.

Peek, H. M. and T* L. Hill, "On Lattice Theory of the Liquid State," Journal of Chemical Physios* X7XII (September# 1950) J m ? r ~ — *

Perkins, G. and others, "Self-diffusion in Molten PbCl2,H

Journal of Physical Chemistry* MIf (Hot ember, I960), 1792*

Perkins, G. and others., "The Diffusion Coefficients of the Pb-210 and Cl-36 in Molten PbClg-KCl Mixtures in the Vicinity of the Composition 2PbCl2*KCl," Journal of Physical Chemistry. IXIV (December, 1960)7WET —

Chemical

feassian, J* H. and 4* H. Kahn, wBlectronio PolarissaMlities of Ions in Crystal®^ Physical Review, XCII (lowmber, 1953), 890.

frioklefeaek, S* S», L. Mania and J# 0*1* Bockris, "Diffusion in the System Molten Sodium Iodide-Potassium Chloride," Journal of Physical Chemistry» LXVIII (January, 1964), 58.

Van Arts&alen, S. 1. and I. S* Yaff e, "Electrical Conductance and Density of Molten Salt Systems? KCl-LiCl, KCl-IaCl and KC1-KI,M Journal of Physical Chemistry. 1*11 (Pabruary. 1955), 118* ~~

Van Artsdalen, 1* 1* and others, "Self-diffusion in Molten Sodium Nitrate.» Journal of the American Chemical Society. LXXVIII (May, 1956),"1772:

Wallin, L. B., «Self-diffusion Measurements iW^polten Salts," Zeitschrift fur Haturforachung« 17a (Pehri&ry, 1962), 191*

* "Zinc Ion Self-diffusion in Eolteu Zinc Bromide," Zeitschrift fur laturforaehung, 17a (February, 1962), 195*

Wallin, L. I. and A. Lunden, »Self~diffusion of 2i.no in Molten Zino Bromide «w Zeitschrift fur laturforachung* 14a (March* 1953), 262. * *

56

Encyclopedia Articles

green. H. S»,,«The Structure of Liquids," Encyclopedia of Physios.- Vol. X, Berlin# Julius Stringer, 19W.

Unpublished Materials

Lu, C. C.» "Sodium Ion Self-diffusion in Molten Mixtures," unpublished Bmster*s thesis, Department of Chemistry, Horth Texas otate University, Denton, Texas, 1963.

Wlmberley, J. f.t "Diffusion of Pb-210 and Cl-36 in the Molten PbCl2-$aCl System," unpublished master's thesis, Department of Chemistry, Eorth Texas State University, Denton, Texas, I960.

fin, H. S. !•, "Diffusion of Ka-22 in ths Molten PbGl2~NaCl System," unpublished master's thesis, Department of Chemistry, North Texas' State University, Denton, Texas, 1962.