HAROLD F.MASON
706
Vol. 61
TIIE KINETICS OF REACTIONS OF SOME ALKALI HALIDES I N THE SOLID STATE’ BY HAROLD F. MASON^ Contribution from the Chemistry Department, University of Wisconsin, Madison, Wisconsin Received February 11, 1967
The rate of reaction between solid powders of certain alkali halides has been studied at about 450’. The rate was foln = m lowed with X-ray measurements and found to fit the formula 1 x = ( G / T * ) 2 l / n s exp( - n W ) which is based on the
-
+
n=l
+
diffusion of ions into spherical particles. The reactions were KC1 NaBr and CsCl KBr. Data of Wood were used to calculate the rate of the reaction NaI KBr. Thermodynamic considerations are discussed. The kinetic data are explained on the hypothesis that the rate of reaction is determined by the diffusion of the cations followed by a slower diffusion of the anions.
+
Introduction described by thermodynamic data for the pure The equilibrium phase relations of reciprocal phases. When true equilibrium exists in a heteropairs of alkali halides have been investigated by geneous system, thermodynamic equilibrium will Wood and co-workers.8 Stable salt pairs were exist internally within each phase as well as exidentified by the X-ray diffraction patterns of the ternally between the different phases. A situation crystals resulting from quenching the mixed melts could conceivably occur in which the various solid and from extensive reaction in the solid state. In phases are not in internal equilibrium (because the 57 of GO reciprocal salt systems studied by quench- crystal has many defects and is thus an “active” ing from the mixed melts complete reaction oc- phase) but in which any reaction between phases as curred and gave the stable salt pair. The stable they actually exist (without changes of defect phase pair consisted of crystals of the smaller character) will be accompanied by zero change in cations coupled to t,he smaller anions and the free energy. This metastable state would be one larger cations coupled to the larger anions. The of “external equilibrium,” but might be identified final product phases were nearly pure binary ,wilts. experimentally as a true equilibrium. Thus therOf the systems studied here, all showed a quenched- modynamic data for pure crystaIline substances melt composition close to the stable salt pair, should be used with reserve when predicting However, Wood, et al., found that the CsBr-KCI equilibria in solid-solid reactions: and a state of rJystem displayed partial reversal and true equilib- “observed equilibrjum” may depart from the state rium when reacting in the solid state for 36 hours of true equilibrium because of the participation of “active” phases. at 400”. The CsCl-KBr reciprocal-salt system presents I n this work the kinetics and mechanisms of three solid-solid rcac tion systems of alkali halides an interesting example of equilibrium because of have been stmdied by X-ray diffraction, NaBr- complete miscibility of reactant and product KCl, CsC1-KBr and Nal-KBr. The spacing and phases containing a common cation. Thus, in the KBr = CsBr KCI, there are intensity of the X-ray lines wcre measured and al- reaction CsCl lowance made for the formation of solid solutions, only two phases, a solid solution of CsCl and CsBr Since the phases resulting from solid-state reactions and a solid solution of KBr and KC1. At equilibfrequently contain crystal defects, thermolumines- rium only two phases exist, and, from phase-rule considerations, equilibrium should be possible cence studies also were made. Thermodynamics.-The thermodynamics of under a variety of conditions. Reaction Kinetics.-The general factors governsolid-state reactions are those for heterogeneous systems of a multiplicity of solid phases, together with ing kinetic laws for solid-solid reactions are (1) any participating gaseous or liquid phases. Except the rates of transfer of material between phases for reactions involving gaseous or liquid phases, and chemical reactions a t phase boundaries, (2) or those in which solid solution of reactants and the rates of diffusion of reactants, and (3) the products occurs, equilibrium is usually not possible rates of nucleation and recrystallization. The form and the reactions proceed exothermically to of the over-all kinetic law will depend on the relative completion,‘ giving the stable salt pairs with rates of these processes; frequently one process smaller cation combined with smaller anion, and will be rate-controlling. The formal statement of any kinetic law will also depend upon the geometry larger cation combined with larger anion. For systems which are exclusively solids, equilib- of the reacting phases and the spatial and temporal rium requires a free energy change of zero for re- sequence in which the various phases appear. action between phases as they actually exist. Thus the mathematical form of the rate equation These phases may be solid solutions and thus not for a reaction in a mixture of powders may be different from its form for the same reaction between (1) Further details of thirr investigation are available in the Ph.D. two parallel slabs of the reactants.Sp6 In this work thesis of Harold F. Mason, filed in the Library of the Univeraity of we are concerned with the laws for powder systems. Wiaconsin, Madison, Wisconain, 1964. (2) California Research Corporation, Richmond, California. Powder systems are treated here by considering
+
(3) L. J. Wood, et at., J . A m . Chem. Soc., 66, 92 (1934); 67, 822 (1935); 66, 1341 (1030): 60, 2320 (1938); E l , 766 (1940): 66, 12ij9 (1944); 74, 727. 2355 (1952): J . Sch. Sci. and Math., 46, 623 (1945). (4) G. Tammann, 2. anoru. Chem., 149,21 (1925).
+
(5) W. Jost, “DiRusion in Solids, Liquids and Gases.” Academic Press, Inc., New York, N. Y., 1952. (6) B. Serin and R. T. Ellickson, J . Chrm. Phyu., 9, 742 (1941).
KINETICS OF REACTIONS OP SOLID ALKALIITAT,IDES
June, 1957
the rcnct,ion ratc to be governed by radial diffusion into spherical grains. Although these assumptions cannot bc rigorously correct, the data obtained correlnt,c with the functions derived on the assumption of spheres. Exact physical significance should riot t x attached to the parameters. 01)the assumption that diffusion occurs into (or (111t of) homogeneous spherical particles of radius, 0 , the rate law may be d e r i ~ e d lfrom , ~ Fick’s first and second laws and expansion through a Fourier series
79”
loo{
060
4
0
/
02
04
06
08
10
12
.
14
--7
16
I0
kl.
Fig. 1.-Calculations
where
for radial diffusion into a sphere.
28 from 20 to SO’) with thin sections of owder preparations mounted flat against a glass surface; a scanning speed of 0.2”/minute with the same technique (scanning a few key patterns to detect the presence of solid solutions); and (3) a scanning speed of 0.2’/minute with powders in random orientation in thick preparations ap ropriate for intensity measurements (for the KCI and k B r 200 reflections). ‘I‘hc derivation implicitly assumes that diffusion Technique (1) was used for identification of phase8 and \vi11 occur with an average diffusivity D through measurement of unit cell dimensions. Technique (2) gave a detailed description of any solid solution formation bcany matrix of phases (e.g., reactant and product) tween the KCI and KBr, and the NaCl and NaBr phasea; within the grain. This, is, of course, an approxi- this was required for a qualitative description of reaction mation, and averages diffusion through crystals, mechanisms and for quantitative interpretation of intensity patterns. Technique (3) was used for the measurement of dong their surfaces, and through microcracks. Values of 1 I were calculated by means of a relative intensities of the KCI and KBr 200 reflections; this gave a measure of the extent of the reaction. Because Card Programmed Calculator (IBM Model 11) they were diffuse, the NaCl and NaBr patterns were not for various values of the exponential’ and are plot- used. Studies of the CsCI-KBr reaction system were only ted it) Pig. 1 where x is the fraction of diffusion quulitative. For intensity measuremcnts by method (3) the pawder completcd a t time. was packed in an aluminum specimen holder similar to that Experimental rocommended by the General Electric Company, to amlire Aft,cr fiisioir i ti a plnt,inum crucitilc, canh piirc rc:tct,ant random orientation of the cryst>als; tthe depth of t8hepackr:ilt W:IR poilrcd iiit,o :I cleaned platinum dish and allowed t,o ing was such that virtually corn lete ahsorption of X-ray8 t,iystnllixt: ti.iid cool to room t8cmperature. The solid mass occurred at thc hack facc.8 TLc scale deflection of tho camera waR calibrated against actual diffractled intmcrifiity. \viis grourid i n a niiillite morttw a i d fiiovod finer than 200 I T . S. Stantlard. Prior to each grinding, the mortar was Diffraction patterns obtained hy technique (3) ahovc werc regraphed to give a linear plot of intensity uersu-s 28 on the Iinnt,cd on ail electric plet,e to prevent pickup of moisture. S i w t d fialts wcre Int,cr subjected to a microsco ic count of basis of this calibration curve. I n the solid state reaction, of NaBr and KCI, scpttrate I)artirlr size. Powder8 of each rouctant were t t e n weighed KBr and NaCl phases are formed. If these phri~eswcrc l o oht,:tin equimolar mixtures. The individual snlts were retlricd at, 125’ and stored in a desiccator until used. Imme- each pure, relative intensity measurements of tho KCI and tlint8elyprior to use the individual reactants were thoroughly KBr 200 reflections would dctermine the extent of reactZion. However, some solid solution occurred between the NaCl rniscd i n a dry box. Rolid-stat,c reactions wcre pcrformed in a Lindhergh and NaBr and between KCI and KBr, as shown hy tho patniiiffle fiirnacc, with automatic temperature control. Meas- terns from techniques ( 1 ) and (2). On the basis of the paturcd temperatures wcre calibrated against a platinum to tern obtained by technique (2), the intensity curve from method (3) was arbitrarily subdivided into three “phnsw”: pl:itjiniim-lO% rhodium thermocouple. During all solidfiolitl rcact,iona, and for at least 30 minutes before each ex- pure KCl and ICBr phaseR, and an int,ermediate solid soluperinlent,, n &cam of high purity, dry nitrogen waR passed tion, the average unit. cell dimension of which was taken as an average for the measiired solid solution int,ensities (cstit,hrorigh the fiirnace, purified by passage through a coppermated from hoth types of patterns taken together). Such a copper osidc heater and a hed of Dricrit,e. Rarh scrips of expcrirnent,s was performed with portions hreakdown is shown in Firz. 2. Here the avcrare unit cc,ll dimension of the K(C1,Brrsolid solution corresponded t.o a of thc snmr rcnctnnt niixt#iire. Scveral s a m p l ~ sin porcelain 27.65. .. ...af .. . .t-rricihlcs Ivrre pl:irrd in t,he furnace n t the snme time and .29 valiie The intnnsit,ies of the t,hrPc arms w r w dct#rrminctl I)y rcrnovcri :i,t npprol)ii:tt,c intervals. The partinlly reartetl niist,iiros wvi-c nllnwctl to cool to room t,nmprrat~urci n R plnniinetcr. Thc arca of the composit,c solid-stilrit.ion region drsicr:bt80r, n.nd t h r n storcd i n n t,ightly mtlcd 1a.r i n a I d of w:is apportioned to KCI and I t n r on t)he hasis of it,R nveragc J ) r y l w util.il n.ti:iI>vis. Thv jar rorit:tinctl a Iwd of Dvicritje. i i i i i t rcll diincnsion a and tho assumpt,ion that, n is R linrnr furirl’ion of molar romposit,ion for KCI-KUr solid solutions.3 l ’ ~ r l i t - i ~ l i iciirc r w:is t,:~lirni n sci,ics T1 t,o assure ra.pid X-ray JII the aliovc cxamplr R 28 of 27.65 correspoiids t80an a of nrlillysls. Rcnrt,intis w t w follo\vctl I)y X-r:i,y t l i f f i w t , i o n , usiiig :I 6.447 A . or 45.8 inole % KCI i n K(CI,i3r). ’I‘hrse apporGrncral I ~ ~ l i ~ tSrIi1c1 ) 4 S-rnJT difira.t!tomctcr. Iiitcnsitics t.ioned areas were added t,o t3hearcas for t,lie rcspcctive lire “phases” to ohtain total KCl and ICBr intcnfiitics. of diffrac,tetl X-ray beams were measured hy a GeigerRlriller oountvr and recorded hy mcans of a potcntiomet8er 4S.8% ,!o the IC(CI,Br) area is added t,o the area of the ICCl s h i p rerorder. Instriimcnt crrors in diffraction angle, 28, “phase. The tot’al intensities were then used t o determinc rd 1 were corrected by calibration with standard samples. Cop- the extent of reaction by comparison with ~ t ~ a n d a mixtuv of react,ants and products. per K a radhtion was iised throughoiit,. For samples of hent,-t.reat,ed Nal3r-1ACI!ION
l'iiro KBr
Tiirir,
hr.
IC0
K(CI,Rr)
hrc I< IiCl (C1,Zlr)
'i'olnl
intensity IiBr KCI
Alolr
28
%ItCl
a
Scrics A 5.67 7.95 1.78 5.67 8.40 2.05 14.00 8.05 0.51 24.25 12.22 .69
4.11 3.50 3.82 5.73
1.51 4.13 1 . 1 1 5.38 2.71 3.73 2 . 0 0 3.30 4.14 1.16
3.16 4.20 6.34 5.54 9.88
27.80 27.83 27.70 27.52
6.412 6.404 G.43G 6.477
60.7 G3.5 52.G 38.6
0.57 0.68 10.70 15.74
4.27 4.28
6.413 6.442 6.447 6.470 0.481
60.4 50.5 48.8 41.0 37.2
2.76 0.04 3 . 1 9 7.50 5.06 0.82 5.27 5.57 10.34 4.84
2.52
Z.DO
Scrics B 0.05 1.00
3.93 6.55 12.32
F R A C T I O N OF LC
27.80 27.67 27.65 27.55 27.50
TABLE 111 REACTION C O M P L E T E U A N D ICINETIC THE N i t B r KCI REACTION
+
= frwtion rcaction complcted, as calcd. from ~ n t c n n i t ~ yIntcnvity
Tiittc,
Iir.
Intensity IlBr
Intrnsity KCI
5.67 0.4G3 0,520 5.67 ,470 ,519 14.00 ,525 .715 24.25 .855 .G75 0.95 1 .90 3.03 5.55 12.32
1)ATA F O R
Int,ensity KCl
Scrics A 0.498 ,409 .G51 ,710
Scrics B 0.177 .I68 .162 ,239 ,280 .296 ,380 .457 .488
0.140 0.310
,161 ,295 .268 .500
2iE-
_IccIIntcnsity IiBr
;;t,"o. tion POIII-
ploted
kl
0,485
,507 0.494 0 ,292 .G4O .G33 , 553 .711 ,738 , 854 0.175 0.201 0.038 .165 .IF4 ,025 ,280 ,274 ,071 ,311 ,104 .298 ,509 .480 .281
Fractions rc:tctod arc givcn as read from corrclat~ionswith integrated intensities of KBr, KCI and thc two rat8iosof thcsc int,crisitics (sec Expcrimcnt,al s c h o n ) . Thew four calculations arc thcn avcritgctl to give the figurcs in tlic next to tlic 1:tst column atitl from thcso the c:orrcspontliny v:thirs of kt arc obtirincd from Fig. 1 anti niorc accurately from tahlcs coiit)aining numcrical valucs c:tlcu[:ttetl by eq. 2. The data are corrclatcd with eq. 1 rewrittcn as
wherc k is a ratc constant. If the assumptions made in the derivation of this equation are obeyed rigorously, the rate constant IC equals 7r2D/a2and thc cquat8ionreduces t o cq. 1. Rinrc! tlic physicd motlcl is only npproxirixttcly rc:tlincd, k: i R : & t i cmj)iricvLI rrttc wiist:trit, arid tlcl)cvids in fact, oil t8fic: pt,~y):tr:ttiotia ~ i ds1,ritcturo of i,iic cryst,:tIS.
A
Y
TABLE I1 INTl':NHITIES O F n I F F R A C T I O N R1~:FLECTlONS
B
/ OB0
/ Y
Sme1A
/
060
r'
/
-x-
- --
HAROLD F. MASON
800
to the face-cciitcrcd c u l h systcm a t 451 f 5°;10Jt cesium bromidc is not rcported to undergo similar transformation. The CsCI-CsUr solid solution crystallizes in the bodycentered cubic system throughout the entire range of solution. Data of Wood, et al., and of this research indicate that the Cs(C1,Br) and K(C1,Br) phases resulting from solid reaction do not form solid solutions with each other. Expcrimental results with a powder mixture, sieved between 200 and 235 U.S. mesh, are summarized in Table IV.
TABLE IV REACTION OF SOLIDSTATEAT 455’
PHASES PRESENT AFTER PARTIAL
KBr Reaction time, hr.
I N THE
Productam o in A.
cscl A N D
No. Molar % lines CsBr in idensolid tiEed soln.
Phase
4.187 f 0.010 CsCl 3 31 4.274 f .007 CsBr 4 72 6.596 i ,008 IlBr 6 6.302 KCI 2 14.00 4.237 i ,002 Cs(C1,Br) G G6 KRr 6 6.590 i .010 6.320 f ,004 KCI 2 24.25 4.2GO f ,013 Cs(C1,Br) 4 79.6 6.565 i ,013 KBr 4 6.307 i ,005 KCI 2 Data of Wood, et al., a t 480’ 36 4.255 Cs( C1,Br) 76 72 4.262 Cs(CI,Br) 78.9 The cell dimensions a for tho pure phases are as follows: CsCl = 4.123R., CsBr 4.200A., KBr = 6.590&, KCI = 6.297 R . 5.67
-
The per cent. CsBr in solid solutioii is c:tlculated from the cx erimentally determiricd value of a. b h e results are similar to those of NaBr-KCI exccpt that CsCl and CsBr form a single mixed phase much more ra idly than the other salt airs. Aftcr 5.67 hr. a t 455’ four plases are present-pure I!Cl, pure KBr and CsCI containing some CsHr in solid solution, and CsBr containing some CsCl in solid solution. After 14 hr. the KBr and KCI phases are still distinct, but the CsCl and CsUr are now mixed to give n single solid solution containing 68 mole % CsBr. After 24.25 hr., the KCI and KBr phases have mixed slightly and the cesium halide solid solution contains 79.6 mole % CsBr, close to Wood’s value for equilibrium. At the reaction temperature, 455’, pure CsCl is very close to its temperature of polymorphic transformation. A phase undergoin polymorphic transformation is hi hly reactive;’” thus e!t reactivity of and the rate of dffusion through the CsCl phase should be greatly enhanced. This seems to be borne out by the rapid formation of the Cs(C1, 2 00.
100-
I20 If.
ow.
04a
c w 0
Vol. 61
Br) solid solutioii and thc rclativcly rapid rate of the over-all reaction. It was not possible to calculate rate constants because Xray intensities were not measured. The products with four phases were more complicated than had been anticipated. The Reaction NaI-KBr.-From solid solubility data given by Wood, et al,a and by the International Critical Tables,lo it ap ears likely that extensive miscibility occurs between all saE pairs except the stable pair, NaBr-KI, a t tern eratures above 500”. g o o d , et al., report data for t p conversion of NaI and KBr to the stable salt pair a t 510 Conversions were eetimated from X-ray intensities of reactant and product phases. Taking their results, and calculating kt by eq. 2 above, the data of Table V are obtained.
.
TABLE V KINETICDATAFOR THE REACTION NaI DATAOF WOOD,et al. Reaction time, hr.
0.5 2.0 15.0 30.0
+ KBr BASED
ON
Fraction completed
kl
0.20 .35 .80 . 00
0.036 0.132 1.123 1.750
The valucs of kt w e plotted again 1 in Fig. 5. The valuc of k for the rcaction is 0.0744 hr.-l. The point a t 00% conversion is highly uncertain since small errors in x yield relatively large errors in kt and estimates of z itself become increasingly difficult when x approaches unity. Thermoluminescence Studies.-Product phases resulting from solid-solid reactions often are “active phases,” rich in defects and possessing unusually high energy contents. Accordingly certain of their physical properties may be affected: magnetic susceptibility, adsorptive properties and catalytic activity. One physical property of dcfect solids is thermoluminescence.1a-15 Thermoluminescence peaks are displayed by many irradiated alkali halides.18 I n addition, after irradiation, many of those salts display colorations and absorption bands characteristic of F-centers. It seemed of interest to investigate any thermoluminescence effects that might be associated with solid-st,ate reactions, and any enhanced thermoluminescence that might be due to the presence of “activc phases” among the products of such reactions. Quantitative studies were made of the integrated inteiisities of glow curves of the partially reacted NaBr-KCI system. Results are given in Table VI, where data are given also for the products and reactants. Areas were obtained by integrating areas under composite peaks covering the entire glow curve from room tern erature to 300”. The temperature is the temperature of the maximum of the major (usually KCI) peak in t8heglow curve. Samples were irradiated for five hours in a cobalt-60 source, receiving approximately 25,000 roentgens. The thermoluminescent activities of the reactant and product mixtures were due almost entirely to KC1 and NaCl. KCI has one sharp eak a t 120’. NaCl displays thermoluminescent activity From 105 to i 7 0 ” . The KCI 120°, NaC1,105P and. NaBf 108’ peaks are coincident and cannot be distinguished in a mixture. In all reaction mmples, only one peak could be distinguished hetwecn 105 and 1:30”, roincident with the KCI, NaCl and NrtRr pcakfl in this rcgion. No thermolumincscence was observed bctwceii 140 and 270”, the temperature rnnge of the high-temperature NaCl peak. Tem eratures :tt which tho peak8 occurred wrre clomly rcproducibe. Integrated intcnsitics are plottcd against time of motion i n Fig. 6. As the reaction time of the mixture increases, the intensity falls off from its iiiitial vnlue to a valuc somewhat above that of the product mixture, KBr NaCl. The total change in intensities is 85% of the ovcr-all decrease from reactants to produce, while over the same in-
+
4
8
1%
Tim. HI
Fig. 5.-Correlation
of NaI
le
20
24
28
32
+ RBr reaction a t 510“.
(10) “International Critioal Tables,” Vol. I, Vol. IV, McGraw-Hill Book Co., Inc., New York. N . Y., 1926 and 1928, p. 352. (11) 8 . Zerncrwzny and F. Rambach, Z. onoru. Uham., 6 6 , 4 0 3 (1910). (12) J. A. Hedvall, “Rcaktionsfahkkcit foatdr Stoffe,” J. A. Rarth, Idprig. 1038.
(13) P. Pringaheim, “Flrloreacence and Phosphorescence,” Interscience Publiahere, h a . , New York, N . Y., 1949. (14) J. T. Randall and M. FJ. F. Wilkinr, Proc. R o y . Soc., (London) 8184, 388, 390 (1945). (15) F. Seitz, “The ModPrn Theory of Solids,” 1st ed., McOrawHill Book Co., Inc., New York, N . Y.,1040. (18) L. Heckelsberg and F. Danicle, THIR J n u R N A l , , 61, 414 (1957).
KINETICS OF REACTIONS OF SOLIDALKALIHALIDES
June, 1057
80 1
TABLE VI
1’1IERMOI,\l MI N E
REACTED hlIXTUREB
X ICNCE: O F PARTIALIdY
OF SanipIo
IW1 A N D NaBr
Time. hr.
Fraction reaction Temp. of completed peaks, “ C .
Tbermoluinincsoence intensityd
Unreac ted
KC1 KBr NnOl NaBr illixcil I iwt:tiits“ Mi x w I prodr~cts~
120
7440
105-270 108 125 105-270
3760 460 5550 1480
Partially rcncted KCI + NaHr 0 . 9 5 0.2Olc 130 5010 1 . 9 0 .I64 120 4500 3.93 ,274 105 3060 5 . 5 5 .324 105 1930 12.32 ,489 106 2020 50 mole % NaBr. * 50 mole % 50 mole % ’ KCl Kl3r 50 mole yo NaCl. Fraction reacted calculated froni X-ray measurements in scries B. * Area on thermoluminescence glow curve (intensity versus time) in arbitrary iinit,R.
+
+
terv:il of rcnction times, the solid phases reacted 48.9y0(by X-rny diffraction). Independent studies of the thermolutninesccnce of solid solutJionsof KBr in KC1 showed the presence of as little as 0.1 molar yo KBr reduced the intensity of the 120’ KCl peak t o less than one tenth of its value for iurc KCl. Thus the disproportionate decrease in tliermolumkwscent intensity with reaction is not surprising and inny bc an indication of a small amount of relatively slow :wiotiic diffusion. Corrclation of reaction kinetics with fractional decrease in I~hernioluminescentactivity, using eq. 2, was not successful. Ikcause of effect,R of small amounts of a second species in ~olitlsoliltion on thermoluminescence intensity, this method docs not appear to offer an attractive means for following solid-Rolid reactions of the alkali halides. The cffcct of “:tctive” product phases might be expected to be shown by maxima in Fig. 6. Such were not observed, wibh the possible exception of a questionable maximum after one hour reaction. Actually, the NaBr-KC1 system is a poor test for any hypothesis of enhanced thermoluminescence rcsulting from “active phases.” The phase giving tho strongest thcrmolurninescence is a reactant phase, KC1; and “activc phases” resulting from solid-solid reactions noultl be expected to be product phases. Such might be t’riie of the reaction between CsCl and KBr, where KC1 is among the products. Glow curves of the partially reacted CsCI-KBr mixture displayed weak thermoluminescence near IOO”, but it remained weak even after 24.25 hr. at 454”. No definite trends in intensity could be identified. The reaction mechanism postulated iiivolves ra id diffusion of both potassium and bromide ions through t i e original CsCl phase, which is highly “active” because the reaction temperature is close t o the temperature of the CsCl polymorphic transformation. Under sur,li conditions, the creation of anything resembling a pure ICCI phase is unlikely; and, indeed, the thermoliiminescence data arc evidence for the ostulated mechanism. In addition, unniixing of any Na&-Iionis shown by the appoara,nce
1
i
9
m0]
~
‘:i“““-;-,6
0 TIME, HR
Fig. 6.-Variation of thermoluminescence intensity wit,li extent of NaBr KCI reaction.
+
of separate patterns of the product and reactant phases, while the slower anion diffusion is apparent from the simultaneous formation of Na(C1,Br) and K(C1,Br) solid solutions. Consider rapid diffusion of potassium ions and a much slower diffusion of chloride ions into a NaBr grain (with counter-diffusion of sodium and bromide ions t o maintain electroneutrality). In the absence of recrystallization the NaBr grain will cont,ain a solution of sodium, bromide, potassium, and (a relatively much smaller amount of) chloride ions. The mixture mill, however, recrystallize to give the stable salt pair, with excess ions going into one phase or the other. Thus NaCl and KBr phases will be formed, with excess sodium and bromide ions being distribiited between the two phases. From independent studies by Daniels and Mason‘ it was found that a mixed vapor of IlCl and excess NaBr crystallizes to give pure KRr and a solid solution of NaBr and NaC1 (up to a t least 62 molar yo NaRr). No evidence was found either in this work or by Wood, et u Z . , ~ for the existence of (Na,K)Cl or (Na,K)Br solid solutions (after quenching). The proposed mechanism, then, involves the formation of IiBr and Na(C1,Br) phases by recrystallization in the NaBr grain. I n similar manner, NaCl and K(C1,Br) phases are formed in the (original KCI grain). The total mixture, then, would contain relatively pure KBr and NaCl phases formed in the original NaBr and KC1 grains, respectively, a.s well as solid solutions of mixed chloride and bromide of a common cation, and the unreached reactant phases. These conclusions are consistent with the X-ray diffraction observations. It is believed that this recryst,allization occurs largely within the origina.1 reactant grains, since the crystals present ,zft8er8,s much as 73.S’r, rmction, possessed tho same olc~,ved,irrcgiila#r habits and part.icle size distribution as the ground, i i n reacted reactant mixtjure, with no evidence of R more regular recrystallizat,ion out’side the origin?: grains. The reaction mechanism is also consistent wit,’, the observed thermoluminescence phenomena.. The total intensit’y of thermoluminescence of the irradiated NaBr-KCl mixture could decrease from the value for the reactant mixt
