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J . Phys. Chem. 1991,95,7050-7054
Single and TweStep Catorlmetdc Studies of Crystalltzation Kkretiee in Simple Ionic GlastiForming Liquids. 1. Ca(NOs)2-KN03 System H. Senapati: R. K. Kadiyala,t and C. A. AngeU**f Department of Chemistry, Purdue University, West Lufayette, Indiana 47907, and Department of Chemistry, Arizona State University, Tempe, Arizona 85287 (Received: February 20, 1991)
Isothermal calorimetric studies of crystal nucleation and growth processes in the aqueous LiCl-H20 system and the model glass-fdng ionic system Ca(NOJ2-KN03 have been investigated. For LiCl-H20 it is demonstrated that the results o b t a i i by using emulsion samples, which protect against heterogeneous nucleation artifacts, can be reproduced by using bulk samples. For the Ca(N0J2-KN03 system some interference from heterogeneous nucleation is observed, but results of character rather similar to those in LiCI-H20 are obtained. These are refined by the use of two different two-step observation schedules which probe the relation between nucleationdominated and growthdominated regimes. The results make it possible to compare the crystallization kinetics in aqueous solutions and ionic melts and contrast them with molten fluoride systems of previous studies.
Introduction The phenomenon of homogeneous nucleation of crystals from supercooled liquids has been the subject of theoretical analysis'-' and experimental investigationM for many years. Normal high-fluidity liquids tend to crystallize suddenly and rapidly within a narrow temperature interval not far below their equilibrium freezing temperatures. The very rapid crystallization rates make it difficult to carry out detailed study of their crystallization kinetics. In glass-forming liquids, on the other hand, growthlimiting viscosity chara~teristics'~make it possible to control the kinetics of crystallization and thereby subject it to systematic experimental observation. For the study of homogeneous nucleation kinetics, it often becomes necessary to use emulsified microdispersed samples in order to minimize the possibility of heterogeneous nudeation. In this manner, the homogeneous nucleation and crystallization of metals, metallic alloys, and water-in4 micdiispersions have been studied.'*I4 More recently, the supercooled LiCI-H20 system has been studied by a variety of techniques including conductivity and differential scanning It has been shown that it is possible to follow the kinetics of crystallization of ice I in the supercooled liquid with particular efficiency and fidelity by the use of an isothermal differential scanning calorimetric (DSC) techniqueI5J6and thus directly to determine the classical timetemperature-transformation (TlT) curves. This technique, without precautions against heterogeneous nucleation, has since been applied to the study of a number of system^.'^.^^ In a more recent study," a two-step DSC technique (a fast analogue of the classical two-stage heat treatment experiment of oxide glaa studies) has been employed to separate the nucleation kinetics from crystallization in emulsified LiCl-H20 solutions. Thereby nucleation curves comparable with those predicted by theory have been observed." Studies of nucleation in this system at higher concentrations have also been made using small-angle neutron scattering2' and fast neutron diffraction techniques on bulk samples, and it has been assumed, from the high nucleation densities observed, that conditions in which homogeneous nucleation predominates have been satisfied. To date, however, this has not been proven. Identification of conditions in which studies on bulk samples would reliably give information on homogeneous processes would be a useful development in this research area, and this has been the initial object of the present work. In this paper we devote an initial section to the comparison of the crystallization rates observed in bulk samples of LiCI-H20 with those in emulsified ones. In subsequent sections we describe how these findings have been used to extend the study of homo-
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P r m t address: Department of Chemistry, Arizona State University, Tempe, A 2 85287-1604. *Present address: Department of Orthopedics, Massachusetts General Hospital, Boston, MA 02141.
OO22-3654/9 1/209S-7050$02.50/0
geneous nucleation and crystallization kinetics by DSC techniques to a nonaqueous ionic glass-forming system,22Ca(N03)2-KN03, which has been extensively investigated as a model glass-forming This system is a favorable choice, not only because of the detailed information available on its liquid-state propert i e P B but also because only one compound crystallizes readily
(1) Bccker, R., Diking, W. Ann. Phys. Stk. 1935,21 (S), 719. (2) Turnbull, D.; Fisher, J. C. 1.Chem. Phys. 1949, 17, 71. (3) Christian, J. W. The Theory of Tranrformations in Metals and Alloys, 2nd cd.;Pergamon Press: Oxford, 1975; Part I, p 418. (4) Avrami, M. J. Chem. Phys. 1939,7,1103; 1940,8,212; 1941,9, 177. ( 5 ) Turnbull, D. J . Chem. Phys. 1952,20,411. (6) Servi, I. S.;Turnbull, D. Acta Merdl. 1966, 11, 161. (7) Turnbull, D. Contemp. Phys. 1%9,10,473. (8) Uhlmann, D. R. J . Non-Crysr. Solids 1972, 7,337. (9) Gonzalez-Oliver,G. J. R.; James, P. F. J. Non-Cryst. Solids 19M, 38, 39, 699. (10) C l a w , D.; Broto, F. J. Phys. Chem. 1976,80,4251; Colloid folym. Sci., Lett. 1982, 260, 641. (1 1) Taborek, P. fhys. Reo. B 1985, 32, 5902. (12) Penpezko, J. H.; Paik, J. S . J. Non-Cryst. Solfds 1984,61&62, 113. (13) Ramussen, D. H.; Loper, C. R. Acta Meroll. 1976, 21, 117. (14) Franks, F., In Wafer. a Comprehensiue Treatise; Franks, F., Ed.; Plenum Press: New York, 1982, Vol. 7, Chapter 3. (15) (a) Angell, C. A.; Sare, E. J.; MacFarlane, D. R. J. Phys. Chem. 1981,85, 1461. (b) Angell, C. A.; MacFarlane, D. R. Adu. Ceram. 1981, 1, 66. ~.
(16) MacFarlane, D. R.; Kadiyala, R. K.; Angell, C. A. J . fhys. Chem.
._.
1983. 87. . 1094. ~
(17) MacFarlane, D. R.; Kadiyala, R. K.; Angell, C. A. J . Chem. Phys. 1983, 79,3921.
(18) Kadiyala, R. K.; Angell, C. A. Colloids Surf. 1984, I ! , 391. (19) (a) Esnault-Grosdemounge; Matocki, M.; Poulain, M. Mater. Sci. Forum 1985.5.241. (b) Mossadenh. R.: Crichton. S.N.:Movnihan. C. T. Mater. Sci. Forum 1M7, 19&20,-453. . (c) Lemon, 0.; Booichand; P. J. Non-Cryst. Solids 1987, 91, I. (20) (a) Senapati, H.; Angell, C. A. Mater. Sci. Forum 1967, 19620,443. (b) Bouaggad, A. Doctoral thesis, Universitt de Rennes, 1986. (21) Dupuy, J.; Chieux, P.; Calemczuk, R.; Jal. J. F.; Ferradou, C.; Wright, A.; Angell, C. A. Nature 1982, 296, 138. (22) Dietzel, A.; Pagel, H. In Proceedings of the 3rd International Congress on Glass, Venice, Italy, 1953; p 219. (23) (a) Angell, C. A. J . Phys. Chem. 1964, 68, 1917. (b) Rawson, H. Inorganic Glass-forming Systems; Academic Press: London, 1967; pp 2 16-2 18. (24) Wciler. R.;Blaser. S.:Macedo, P. B. J . fhvs. Chem. 1969. 73.4147. (25) Howell, F. S.;Bose, R. A,; Macedo, P. B.;Moynihan, C. T. J . Phys. Chem. 1974, 78,639. (26) Rao, K. J.; Helphrey. D. B.; Angell, C. A. Phys. Chem. Glasses 1973, 14 (2), 26. (27) Torell, L. M. J . Chem. Phys. 1982, 76 (7), 3467. (28) Angell, C. A,; Torell, L. M.J . Chem. Phys. 1983, 78 (2), 937. (29) Sidebottom, D. L.; Sorensen, C. M.J . Chem. Phys. 1989, 91 ( I I), 7153.
Q 1991 American Chemical Society
Crystallization Kinetics in Ca(N03)2-KN03 4001
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Figwe 1. Phase diagram of the Ca(N0,)2-KN03system, adapted from ref 23. The symbols denote glass transition temperatures: ( 0 )ref 26; (A) ref 28; (0)present work.
from melts in the vicinity of the eutectic composition in the equilibrium phase diagram;22*23 see Figure 1. This compound, Ca(N03)2-4KN03,crystallizes without yielding any subsequent polymorphic transitions or inducing crystallization of other compounds and hence gives a simplicity of behavior comparable with that of ice I crystallizing from aqueous solutions." The composition range 31.5-34.5 mol % Ca(N03)2was found to provide crystallization rates suitable for study by the present technique.
Experimental Section Sample Preparation. The bulk solution of 9.65 mol % LiCl in H 2 0 was prepared gravimetrically from anhydrous LiCl and distilled, deionized water as described earlier.l6 Samples of the solution were emulsified in a noncrystallizing 1:1 methylcyclohexantmethylcyclopentane mixture with Span 65 (sorbitran tristearate) as Differential scanning calorimetry experiments were performed on -3O.mg samples of bulk solutions or emulsions, contained in hermetically sealed aluminum pans. Ca(N03)2-KN03 samples were prepared from 99.99% KN03 (Mallinckrodt), and anhydrous Ca(NO3)z obtained by dehydration of reagent grade Ca(N03)2-4H20at 200 OC to a constant weight in a vacuum oven. In order to avoid moisture absorption, the anhydrous Ca(N03)2 was weighed out in a tightly stoppered weighing bottle; the requisite amount of KN03 then added to it, and the mixture melted on a hot plate. A drop of the homogeneous melt (-50 mg) was placed in an aluminum pan which was immediately mounted into the sample chamber of the DSC and held at 470-500 K in an atmosphere of dry nitrogen for a period of 5-10 h, to ensure that residual traces of moisture could escape; the sample was then used for calorimetric studies. Some studies were done on samples that were held at 500 OC for up to 24 h in order to check that the period of dehydration has no effect on the crystallization peak times. In the latter series of investigations, the sample was cooled to 300 K inside the glovebox after a 12-h period of dehydration at 500 K, and the pan was sealed under the nitrogen atmosphere. A single sample thus prepared was then used repeatedly to complete both single- and two-step calorimetric studies on a given composition. clsoriwhicTccwquCa The singlestep TTT experiments on bulk and emulsion samples of LiCI-H20 were performed using the Perkin-Elmer DSC-2differential scanning calorimeter in the manner reported earlier in the detailed study of this system.I6I8 The same instrument and a similar procedure were used for the nitrate melts, which were quenched from 490 K at the maximum cooling rate attainable with the DSC-2, to a preselected temperature of observation, and the evolution of the crystallization exotherm was recorded as a function of time. An initial TTT study was carried out on a 3 1.5% Ca(N03)2 melt using the same instrument head (Model DSC-2) as that used in the study of the LiCI-H20 system. All subsequent studies were performed with a different (though nominally identical) instrument
1.2
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Figure 2. Isothermal crystallization peak times fp at different temperatures (TTTcurves) for the 9.65% LiCI-H20 solution: a comparison of results for bulk (m) and emulsified (0)samples. Note excellent agreement of rp values tetwcen the two kinds of samples. The arrow in the insert shows definition of .1, head which exhibited a somewhat slower response time. The time spent in passing between the liquidus temperature and the temperature of observation varied between 15 and 30 s, depending on the temperature of observation. The characteristic time for crystallization,t, was taken as the time required to reach the peak of the crystallization exotherm (see insert to Figure 2). This has been shown elsewhere to correspond to 45 vol 5%of ~rystalliition.~~ After some irreproducibility, presumably due to heterogeneous nucleation interference, was detected in the early studies based on separate preparations by separate investigators, a serial study based on successive modifications of an initial Ca(N03)2-richmelt was carried out. The results are presented in sequence below. To help distinguish the effects of nucleation kinetics from the combined effects of nucleation and growth, two-step experiments were carried out on the slowest crystallizingcomposition for which In a TTT curve could be obtained [34.3Ca(N03)2-65.7KN03]. the first type of two-step experiment intended to determine the temperature at which the nucleation rate is greatest, the melt was quenched from 490 K to a preselected temperature of nucleation TI and held there for a fixed period of time 1, (30 or 60 s); the temperature was then raised (at a rate of 320 K/min) to a fixed temperature of growth T2 where the crystallization peak was recorded. (In a later presentation of results, we will represent a given selection of these parameters by the notation (T,/rn/T2).) Note that this is simply a speeded-up version of the classical optical microscopic e ~ p e r i m e n t in s ~which ~ a nucleation period at some temperature of interest is followed by a growth period at a higher temperature after which the nucleation density is determined by counting the growing crystallization centers. In a variation of this two-step sequence, intended to permit study of growth rates at constant nucleus density, tp measurements were made at various growth temperatures T2after a 30-s nucleation period at afixed temperature of nucleation T I (at which the nucleation rate had already been found to be the greatest). In this experiment, four different rates of heating from TI to T2were tested to check whether or not nuclei generated at TI were being redissolved in the process of heating to T2. ReSultS Bulk and Emulsified UCI-H20 Solution. Figure 2 shows a comparison of the crystallization peak times ( r ) at various temperatures (the TTT curve) for bulk and emukifed samples of ' LiCI-H20 solution. It can be seen that these peak the 9.65 mol % (30) Christian, J. W. The Theory of Transformaffons in Metals and Alloys, 2nd 4.Pergamon ; Press: Oxford, 1975; Part I, p 542.
7052 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 460 440
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FIgm 3. TIT curva for Ca(NOJ2-KN03 melts obtained by a one-step isothermal calorimetry technique, using different sample compositions and preparations as indicated in the legend. The error in tp is *2 s where the peaks are sharp near the nose of the TTT curve and A10 s for longer crystallization times where the peaks are broadened out.
times are in excellent agreement with each other in both the nucleation-dominated (upper part) and growth-dominated (lower part) regions of the TIT curve. Since nucleation in the emulsified samples is known to be essentially homogeneous in character,I3 and since the crystallization times for the bulk samples match so well with those for emulsified ones, it would appear that, for this range of viscosities and nucleation rates, the crystallization in bulk samples indeed occurs by a homogeneous mechanism. This is a rather important conclusion because it raises the possibility (not always to be realized) of investigating homogeneous crystallization kinetics in a great variety of systems that are not easily emulsified. CrystallizationKi~eticsin the Ca(N03)2-KN03System. Preliminary work showed that in this system the composition range of 3 1.5-34.5 mol % Ca(N03)2yield crystallization rates that fell within the "window" of our DSC technique. In view of the response time of the instrument head, the more slowly crystallizing samples starting at 32.5% Ca(N03)2and ranging up to the 34.3% Ca(N03)2composition, which lies on the Ca(N0J2-rich side of the eutectic composition, 33Ca(N03)2-67KN03(Figure l), were chosen for detailed investigation. The best glass-forming composition in this system has been shownZ2to be the posteutectic Ca(N03)2-rich composition, 38.1Ca(N03)2*61.9KN03;therefore clearly, crystalline Ca(N03)2requires a much larger thermodynamic driving force to nucleate than does Ca(N03)2-4KN03. Thus, regardless of which side of the eutectic composition the present samples fall, the crystallizing compound will always be the latter. A comparison of results from two series of t, measurements (different instrument heads, different investigators, different sample preparations) for the fastest crystallizing composition that could be studied with each instrument head is shown in Figure 3 (31.0% and 31.5% Ca(N03)*), and the accordance is satisfactory. Another series at 33.3% Ca(N03)2yielded a narrower lower temperature TTT curve, which could be reproduced in a second set of measurements on the same sample. However, subsequent results on other compositions suggest that this difference was not instrumental but rather was a consequence of some source of heterogeneousor surface nucleation. It was noticeable that where the observation temperature was high the crystallization peaks lost the simple form seen at low temperatures and developed a doublqeak structure, suggesting a competition between different sourca of crystallization. Therefore, the lower temperature results are more reliable and probably represent the homogeneously nucleated process. To minimize this influence or keep it constant, the remainder of the study was based on the use of a stock melt of high Ca(N03)2content (34.5% Ca(N03),) to which KN03
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Figure 5. 'Nucleation rate" curve obtained using the two-step technique, with nucleation times of 30 and 60 s. T2 is the temperature where 'growth" of the nucleated samples was observed. Comparison is made with the one-step TTT (nucleation and growth) curve.
from a single source was added sequentially until the high KN03 limit was reached. The TTT curves obtained in this series (in the temperature range 350-400 K)are shown in Figure 4. The data indicate that there is a source of heterogeneous nucleation which influences the upper portion of each TTT curve (which is nucleation dominated). The lower portion, which seems in sequence with the sharp TTT curve obtained in the earlier set of measurements (shown in Figure 3), is presumably the homogeneously nucleated part. It has been separated out by a dashed curve construction. It will be seen subsequently that even the broadest of these TTT plots is still comparable in form with homogeneously nucleated crystallization in the LiCI-H20 system. In Figure 5 are shown the results of the first type of two-step study (T1/t,/385 K) conducted on the slowest crystallizing composition for which a TTT curve could be obtained (34.3% Ca(NO3)*). Figure 5 shows the original "T curve and then shows the shorter times at which the crystallization peak is reached when crystallization is observed at 385 K (the TTT nose temperature) after an initial exposure for 30 or 60 s at a "nucleation temperature" TI. It is the latter temperature which is plotted on they axis of Figure 5 . From Figure 5 we can see that the temperature TNN(-350 K) is producing the most nuclei during the time spent at T I .
Crystallization Kinetics in Ca(N03)2-KN03
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Figure 6. Plot of crystallization peak times observed at different temperatures T2after nucleating the melt at T,= 350 K for 30 s. The plot gives information on the variation of crystal growth rate with temperature as distinct from the nucleation rate. The different symbols illustrate the effect of changing the rate of heating (ramp rate) between TIand T2(see footnote 35). Insert shows an Arrhenius plot of the two-step 1, values in the low-temperature diffusion dominated region compared with the Arrhenius variation of shear viscosity.
Figure 6 shows the results of the second type of two-step measurement (350 K/30 s/T2) and compares them with the original one-step TTT curve. In this case they axis shows the temperature T2at which the crystallization was observed following an initial exposure of 30 s at a fixed nucleation temperature: 350 K, which is the temperature of maximum nucleation rate established in Figure 5 .
Discussion The time taken, t,, for a given volume fraction to crystallize at any given temperature directly reflects the rate of crystallization at that temperat~re.'*~J~ As seen in Figures 2-4, the rate of crystallization increases initially as the driving force for nucleation increases but then decreases at lower temperatures where restricted particle mobility frustrates the growth of the nuclei that form. The nose in the TTT curve thus corresponds to a temperature at which the competing effects balance, and the rate of crystallization reaches its maximum.30 The position of the nose in the TTT curves in Figures 3 and 4 is seen to move to longer times with increasing Ca(N03)2 content, as is consistent with displacement deeper into the glass-forming region (see Figure 1). The Same behavior was Seen in more detail and with less complication in the earlier study of LiCI-H20 solutions.I6 The temperature TN at which the crystallization rate maximizes shows a slight decrease with increasing Ca(N03)2,particularly if one focuses attention on the lower parts of the curves which reflect the homogeneous process. A decrease would be expected from the decreasing temperature for constant supercooling (Le., constant thermodynamic driving force to crystallization) based on the liquidus curve for Ca(N03)2-4KN03 and its metastable extension beyond the eutectic composition shown in Figure 7. On the other hand, an increase of TN would be expected from the increase in viscosity (hence decrease in crystal growth rate) indicated by the increase of T, with mole percent Ca(NOJ2 Scen in Figure 7,which probably accounts for the weak slope of TN relative to that of TL. The proximity of the TTT curve to the metastable liquidus temperature distinguishes this system from the LiCI-H20 system studied earlier and from other glass-forming systems to be described in subsequent articles. To understand this, we must suppose that the nucleation probability rises very rapidly with undercooling, Le., that the barrier to nucleation is small. This implies that in the Ca(N03)2-KN03 system it is only the high viscosity at the liquidus temperature which leads to glass-forming ability. The viscosity at the liquidus temperature of 423 K estimated (see below) for the 34.3% Ca(N03)2melt is 4.0 P.
20
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Mole % Ca (N03)Z Figure 7. Enlarged phase diagram of Ca(N03)2-KN03system showing the position of the nose of the TTT curve TN (both homogeneous and
heterogeneouscases) relative to the liquidus TLand the glass transition temperature TI.TNNis the temperature at the nose of the "nucleation" curve for the 34.3Ca(N03)*sample (filled symbols). The nucleation rate, according to the two-step measurements reported in Figure 5 , is a maximum at -350 K, which is just 23 K above T, (and may be less for the fully homogeneous process because TNfor this sample falls on the TN(het) line in Figure 7). Since T, is increasing with increasing Ca(N03)2content and since the temperature of maximum nucleation rate T" must be decreasing at least as rapidly as TN, it is obvious from the juxtaposition of lines in Figure 7 that the maximum in the nucleation rate curve will sink below TBby the middle of the glass-forming range. This is, of course, consistent with the excellent glassforming properties of the much-studied composition 40Ca(N03)2.60KN03, for which the Ca(N03)2-KN03 system has become well-known. Before leaving this part of the discussion, we should emphasize that the shape of the nucleation curve (Figure 5 ) below the nose is not expected to be accurate because the nose occurs at too short a time to be bypassed given our maximum instrumental cooling and heating rates (320 deg/min) without some nucleation being initiated. The points represent minimum times, and the correct curve shape is probably more like the dashed line in Figure 5. We now address the results of the second two-step experiment shown in Figure 6 and compare them with the observations made previously for the LiCl-H20 system. In principle, the initial exposure at TI, where the nucleation rate is far greater than at T2, should ensure that the observed crystallization rate at T2is little affected by on-going nucleation at T2. Instead, it should be dominated by the rate of growth of the nuclei initially created. Indeed the nucleated samples always crystallize more rapidly than the unnucleated (onestep) samples, though the difference naturally diminishes as T2approaches TI. However, the maximum in the crystallization rate in the two-step experiment seen in Figure 6 (for each of the four different ramp rates35)requires comment since such a maximum is usually due to the dominance of the nucleation rate-which in principle we have eliminated in this experiment. We note firstly that no maximum rate appears in the corresponding experiments for the LiCl-H20 case.I8 The outstanding difference between the two cases is the proximity of the liquidus temperature to the temperature at which the crystallization is being observed in the Ca(N03)2-KN03case. Clearly, when the temperature of observation reaches TL(423 K), the driving force to grow crystals must disappear. Thus, the crystallization peak must move to long times as TLis approached, so a maximum in crystallization rate must occur for T near TL.This has k e n seen directly in the pioneering study of Ca(N03),-KN0, glasses by Dietzel and PoegeL2, These authors measured crystal growth rates for individual Ca(NO3),-4KNO3 crystals and observed a maximum at 392 K for a 34.4 mol % ' Ca(N03)2solution
7054 The Journal of Physical Chemistry, Vol. 95, No. 18, 1991 I
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Figure 8. Comparison of internal relaxation times q,, and escape times T,, (from crystallization peaks) and rmt(nuc) (from two-step crystalmelt at different temperalization peaks) for 34.3Ca(N03)2*55.7KN03 tures. q,, values are obtained from data on photon correlation.29 (A), shear relaxationa (A), and neutron spin echo” (m) for the 40Ca(NOJ2.60KN03melt, waled down by the TIratio (see cq 1). (their 46 wt 9%; see ref 23b), which agrees well with our results. Since, at the lowest temperatures, the value oft, in the twestep experiment shown in Figure 6 is controlled by the crystal growth rate, it is expected that the temperature dependence of t will increasingly resemble that of the viscosity. This relationsfhp is checked in the insert of Figure 6 in which 1, is plotted as an Arrhenius function of temperature. The viscosities ( q ) for the 34.3% Ca(N03)2 melt, which are not known in this temperature range, can be estimated by scaling the temperature from the known viscosity data2‘ for the 40Ca(N03)2-60KN03melt by the ratio of Tg values (327/334). Thus we assume q at
T’for 34.3% Ca(N03)’ = q at T for 40% Ca(N03)2 (1)
where T’= T[327/334]. V i i t y values thus obtained are plotted in Figure 6 (insert) using the same logarithmic scale; the approach of the slope of log [t,] curve to the log [q] curve with decreasing temperature is rather satisfactory. The activation energy for growth obtained from the two lowest temperature points is 354 Id/mol, which is approaching the value 530 kJ/mol estimated for viscosity in the same temperature range. Since the lower part of the nucleation curve in Figure 5 should equally be dominated by the viscosity, our dashed line correction to the observed curve, to remove distortions of the plot due to seems justified. nucleation during cooling past TNN, We now note that the comparisons we have just made are closely related to the comparison of T~ and rat used in our earlier general discussions of crystallization vs vitrification phenomena” (initially in relation to computer simulation studies of glass formation3’). ~b is the time scale for internal relaxation (Le., relaxation within the metastable liquid state), and is the time scale for relaxation out of the metastable liquid state into the stable crystalline state, (Le. for relaxation from one free energy surface to the nearest lower one). All that is necessary to obtain the same comparison is to convert the viscosity data in Figure 6 (insert) into shear ~
~
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(31) Angell, C. A.; Senapati. H.In The Blophydcs of Organ Cry0 reseruarlon; Pops, D.E.,Karow, A. M., Us.; Plenum Res:New York, f981; pp 147-171. (32) Woodcock, L. V.; Angell, C. A,; Cheeseman, P. A. J . Chem. Phys. 3976, 65, 1565. (33) James, P. F. Adu. Ceram. 1981, I , 1. (34) Muei, F.; Knaak,W.; Farrago, B. Phys. Reo. Lcrr. 1987, 58, 751. (35) Thc results of the different ramp rate experiments, which were dcsigned to check whether critical nuclei were being loat on heating, arc indechive. The fp vrlua pbttcd in Figure 6, which arc rhortcr for the lower ramp rates, at ftnt light might IU t that additional nuclei had indeed been praerved, but this ignora the% that nuclei can grow during the ramping period itself, which is longest for the lowest ramp rate. Taking this into account, we judge that the ( “ c t e d ) rp values are more or les independent of ramp rater and the critical nuclew dissolution ia therefom not an important
effect.
