R. P. RASTOGI AND PARMJIT S. BASSI
2398
neighbors and that a t high kinetic energies the equivalent hard-sphere radius might be somewhat smaller than the soft-sphere minimum. The relative values of et* indicate that the increased polarizability of polymer us. monomer niay be slightly more effective in lowering the potential minimum in linear than in curved molecules. ,4n estimate of the contraction per ring due to the removal of hydrogen atonis16a t the ring-ring bond would predict about 6.4y0 lower hard-sphere volume for biphenyl per ring and 8.5% less for the terphenyls per ring. The observed contractions based on r* ratios are 9% and 13%, respectively, for the straight chains. The extra contraction might be due to the increased attractive energy of the polymers over benzene as shown in the E*
values. There appears to be a slight additional volume for the m- and o-terphenyls which could be due to shape hindrances to optimal packing. The apparently anomalous behavior of p-terphenyl compressibility is probably not worth discussing until more is known about the validity of the drastic approximations in the model. Conceivably the molecules as a whole have bending modes which are of low enough frequency so that the vibration amplitudes over the length of three rings are large enough to give the effect of some flexibility within the free volume diameter. (15) L. Pauling, “The Nature of the Chemical Bond,” 3rd Ed., Cornel1 University Press, Ithaca, N. Y., p. 260.
Mechanism of Eutectic Crystallization
by R. P. Rastogi and Parmjit S. Bassi Chemistry Department, University of Goralchpur, Gorakhpur, I n d i a
(Received October 7, 1963)
With a view to elucidate the mechanism of eutectic crystallization, the undercooling and linear velocity of crystallization from binary molten mixtures of naphthalene and phenanthrene have been studied. Microscopic study and heat of fusion measurements were made to investigate the characteristics of the solid eutectic. The heat of fusion of the freshly precipitated eutectic is found to be 20.30 kjoules/mole, a value slightly higher than would be anticipated from the mixture law. The linear velocity of crystallization from the eutectic melt is about low6times the velocity of crystallization from melts of pure components. This furnishes evidence of the precipitation of mechanically separable phases. The microscopic and photomicrographic studies show the different characteristics of freshly precipitated eutectic as compared to the pure components, which are lost on standing. It has been suggested that this is largely due to recrystallization of fine grains.
T h e Journal of Physical Chemistry
8lECHANISM OF
ECTECTIC CRYSTALLIZATION
2399 I
considers a eutectic to be formed by some sort of loose molecular or atoniic interaction which does not involve the formation of a chemical conipound. The forniation of a eutectic leads to some merging of electron energy levels or to electron sharing, but this is not accompanied by the formation of interatomic electrostatic bonds. Savchenko has shown his hypothesis to account for a nuniber of experimental facts. The theory is proniising even though it conflicts violently with the therniodynaniic necessity that the eutectic mixture has only to be a mechanical mixture. I n view of the great technological uses of eutectic alloys, it is desirable that eutectic crystallization should be studied thoroughly. I'or our detailed study, the naphthalene-phenanthrene system was chosen since the iiiixture is approximately ideal. Thus coniplications arising froni the deviations froni ideality would be almost negligible. 'The linear velocity of crystallization and undercooling in melts were studied. Microscopic and photomicrographic studies were made to elucidate the structure of solid phases. I n order to throw light on the mechanism of eutectic crystallization, measurements were made of the heat of fusion of the pure coiiiponenits and the eutectic mixture and the heat capacities of the pure coniponents in the solid and liquid states.
Experimental Materials. Naphthalene (E. llerck, extra pure) was first purified by ordinary distillation and finally subjected to redistillation under vacuum. The purity of the saniple was confirmed by the determination of the melting point, which is 80.3', in agreement with the recent literature value. Phenanthrene was distilled at a pressure of 12 nini. and the distillate was collected between 210 and 215'. It was further purified by fractional Crystallization with ethyl alcohol. The purified phenanthrene was kept in a vacuum desiccator for about 1 week. The melting point of the saniple mas 100.0 i 0.2'. Procedure. (i) Cndercooling in Melts. I n order to study iiiaxiiiiuni undercooling in the molten mixtures, it was necessary to know accurately the melting points of the mixtures beforehand. Hence, the phase diagram of the mixture was reinvestigated by the procedure adopted by Rastogi and Rania Varnia.* The undercooling was determined by the procedure describrd ~ a r l i e r . ~This can be utilized to give a comparative estimate of undercooling for melts of different conipositioiis. Since such an estimate mas needed for the present purpose, niaxiinuni care was taken to perform undercooling experiments for mixtures under identical conditions by keeping the volume of the melt and the
rate of cooling the same in all the cases. The solidliquid equilibrium data and the undercooling data are plotted in Fig. 1.
1 0.2
0 -4
Ma& -1raction o j
0.6
0.8
1.0
Phenanthrene
Figure 1. Phase diagram and undercooling for naphthalenephenanthrene mixtures: 0,melting points; X, temperature a t which crystallization occurs spontaneously; 0 , thaw points.
(ii) Linear Velocity of Crystallization. The experimental technique for determining the linear velocity of crystallization was siinilar to that adopted by Rastogi and Chatterji6 The measurements were made in a Pyrex glass tube 50 mni. long with an inner diameter of 6 nim. and two right-angled bends. It was placed in thermostat kept constant to + O . l o . The rate of advance of the crystal boundary was recorded by a stop watch. The results are less accurate in the case of mixtures near the eutectic ratio, since within the observation time the crystal boundary moved only a very sniall distance which could not be ascertained very accurately. The results are recorded in Fig. 2 . (iii) Microscopic and Microphotographic Investigations. For microscopic and microphotographic studies, slides were prepared and examined under a microscope. (2) P. S. Savchenko, Russ. J . Inorg. Chem., 4, 187 (1959). (3) J. Timmermans, " Physico-Chemical Constants of Pure Organic Compounds," Elsevier Publishing Company, Inc., Amsterdam, 1950, p . 178. (4) R. P. Rastogi and K. T. Rams Varma, J . P h y s . Chem., 62, 641 (1958). ( 6 ) R. Gopal and R. .'1 Rastogi, J . Indian Chem. Soc., 27, 403 (1950). (6) R. P. Rastogi and A. C. Chatterji, J . P h y s . Chem., 59, 1 (1955).
Volume 68,Number 9
September, 1B64
2400
R. P. RASTOGI ASD PARXJIT S.BASSI
3 1
2
1
0 "1
'% 0
kl
-1
-2
-3
-4
J
Figure 2. Linear velocity of crystallization a t various degrees of undercooling: I, pure naphthalene; 11, pure phenanthrene; 111, mixture containing 0.889 mole fraction of phenanthrene; IT', mixture containing 0.200 mole fraction of phenanthrene; V, mixture with 0.295 mole fraction of phenanthrene; VI, mixture with 0.405 mole fraction of phenanthrene; VI& mixture with 0.500 mole fraction of phenanthrene; lX1, mixture with 0.600 mole fraction of phenanthrene; I X , eutectic mixture; X, mixture with 0.685 mole fraction of phenanthrene.
A very small drop of melt was placed on a niicroslide and covered with a cover-slip. The microphotographs of the crystaIlized pure components and their mixtures are given in Fig. 3-8. (iv) Determination of Heat o j Fusion. The details of the calorimeter used for this purpose are given here. A Pyrex glass tube (7.62 ciii. long, 0.84 cin. internal diameter) closed a t one end and having a ground-glass joint a t the other end was used. A weighed amount of the sample was taken. A calibrated thermistor and constantan heater were inserted in the tube which was kept in a long double-walled Pyrex tube connected to a vacuum line. A stirrer with a iiiercury seal passed through the B-24 standard joint. The calorimeter was kept in a thermostat maintained either a t the melting The Journal of Physical Chemzstry
point or the eutectic temperature, depending upon the substance whose heat of fusion was to be determined. The heating circuit consisted of a 6-v. battery, a rheostat, a 1-ohm standard resistance, and an aninieter in series with the heater. The voltage across thc heater and the standard resistance was measured by a Pye precision vernier potentiometer. The temperature of the calorimeter was regularly noted with the help of the previously calibrated thermistor. The heater and the stop watch were switched on when the sample attained the temperature of the thermostat as indicated by a spot galvanometer in the circuit. The temperature of the sample was noted as frequently as possible. The material was slowly and intermittently stirred to prevent the setting up of temperature gradients in the
~ I E C H A S IOF S XEVTECTIC ~ CRYSTALLIZATION
sainplc. The tcnipcratnre rcniaincd constant while the saniplc was niclting. As soon as the tcnipcratnre showed a tcridency to risc, the stop watch and thc heater were siinultaneously switched off. The risc in the tcinperaturr occurrd only after the cntirc sample had melted. Thus, thc tinie for coniplrtc nielting was noted. During nielting, the voltagr across the heater and the standard resistance was nieasurrd several times. Since the tcnipcratnrr of the thermostat was the eanie as the nielting point of thc saniplc, radiation losses were greatly niininiised. In the present casr it was not necessary to nieasure the specific heats of the materials in the solid arid liquid states, since the exact ainount of electrical energy required to nirlt the given amount of saniple can be directly nieasured. I,,, the latent heat of fusion i n joulcs/niolc is given by the relation
2401
2402
where 15 is t h r voltage across the heater, 111 is the weight of the sairiple, tis time iii seconds for coniplete nieltiug, c is thc voltage across the staudard resistauce (current iu the circuit), and A! is tlic niolccular weight of the salnple. I'or calculating the iiiolccular weights, tho stoniic weights of carbon and hydrogen were taken to he 12.010 aud 1.0080 g., respectively. The errors iri nicasuriug voltage, curreut, and time would ouly accouiit for an error of *O.Olyo in the values of heat of fusion at the niost. The principal sources of error i n the ineasureincnts of thc heat of fusion arise froin the following factois. (a) lladiatiou losses are due to the difference in the teuiprrature of the calorinicter and that of the surrouudiiigs. Exprtinients perfornied with the hath teniperaturr 0 . . 5 O higher or lower than the eutectic temperature show that tlic uiaxiniuin error iu the ureasurcments of heat of fusion is of thr order of 2%. This would be considerably lower in our cxperinieiits siucc the tcmperaturc differeiiec was well withiu *0.0.5'. (h) The rcsistrtnce of the heater niay change on accouut of the iiicrease in teinperatrire of the heater wire due to difficulty i u heat dissipacioii in the solid iiiass. I'or estiniatiug this error due to change i i i the resistance of the heatrr, a typical cxporinicnt was performed in which the voltage across the heater was constantly read froni thr potrutionieti.r. ' I hrrsistaricc of the hrater was found to vary within +0,.5%. However, this could he niininiisrd by suitahlc stirriug. Thc error oii thisaccouut is not cxpc,ctcd to he iiiore thau 1%. ( I , ) ,Ileasurei,imls i< Heat Capacilies. Thc caloriinrtcr nsrd for this piirposc was siinilar t o that used for hrat of fusioii iiic,asuri.iiiriits, cxcrpt that haatrrs of diffcrriit drsigiis iwrr usrcl for solids and liquids. The heat,capacity \vas oalculatrd froni the equatioii
R. 1'. RASTOGI ANI) I'AIIMIIT S. I~ASSI
whcre C , is the heat capacity, W is the water cquivaleut of the calorinicter, arid de/dt is the ratc of rise of tcniperature. I'or the nicasurenient of heat capacity of solids, the heater consisted of four plates of copper (each 2.54 cni. lorrg, 1.52 cni. hroad, aud 0.05 cni. thick) joiircd at right angles to each other. Sichrolne wires were wound arouud the grooves on the edges of the plates. The plates were insulated hy coatiug with hralditc. The tcniprrature nieasureineiits were niade with a coppcr-coustantan tlierlnocouplc. Ice in coutact with cold water was used as a cold juiictiorr. In case of liquids, the heating elrmeut was wouud round the grooved edges of a druni-type Pyrex glass tube (2.54 cm. long arid 2.03 cin. internal dianietcr). The water equivalent of the calorinicter was detcrmined in the usual way. The heat capacity of water was taken as 4.1780 at 35". Knowing the value of W , C,, could be determined. The lattcr are correct t o *4%.
( v i ) I'hotometric Study of Solidijicalim of the / h / e c / i c Mizture. The sequence of the changes that a freshly precipitated eutectic undergoes was studied optically. A inicroslide prepared with freshly precipitated eutectic was placed between a photocell and a light sourcc. Froni the latter a parallel beam of light could he ohtained by placing a convex lens of suitable focal length. The changes in theintensity of light falling on the photocell could be estimated froni the position of the spot in a I'ye spot galvanometer, connected iii scrics with the photocell along with a key and a rheostat. The rcsults are given in Fig. 9.
I*
I
d $0
20
30
40
50
t ).UDh(
Figure 9. Rate of rerryetnllirntion of freshly precipitated eutectic mixture.
60
7o
8o
9o
MECHANISM OF EUTECTIC CRYSTALLIZATION
2403
Results The phase diagra,m and the limits of undercooling are plotted in Fig. 1. The linear velocity of crystallization is recorded in Fig. 2 . The examination of microslides with a microscope showed that the solid eutectic had a quite different structure. This ha,d a definite pattern and differed widely from that of the parent components. Figure 7 indicated that white lines are more fluorescent as compared to the black ones. Results of heat of fusion measurements are recorded in Tables I and 11. Those for heat capacity measurements are recorded in Table 111.
Table I : Heat of Funion of the Eutectic Mixture Mole fraction of phenanthrene
Ee, joules
0.4328 0,4328 0,4328 0.4332 0,4332 0,4332 0,4320 0.4320 0,4320 0,4324 0,4324
0,55037 0.5503 0.5210 0.5487 0.5242 0,5210 0.4857 0,4857 0,4968 0.6203 0.5588
Temp. interval,
Bath temp.,
O C .
"C.
Heat of fusion, kjoules/ mole
51.3 51.3 51.3 51.3 51.3 51.3 51.0 51.3 51.3 51.3 51.3
20.1 20.15 20.7 20.1 20.1 20.3 20.8 20.7 20.2 19.8 20.1
51.3-52.0 51.3-52.0 51.3-52.0 51.3-52.0 51.3-52.4 51.3-52.0 51.0-52.1 51.3-52 1 51.3-52.3 51.3-52.0 51.3-52.0
--l/kT
Av. 2 0 . 3 i 0 . 2 5
Table I1 : Heat of Fusion of Pure Components Heat of fusion; joules/g.
No. of
SubB t a n c e
Naphthalene Phenanthrene
149 rt 1 101 i 2
5 7
runs
-
Table 111": Heat Capacities of Pure Components
a
Substance
State
Heat capacity, joules/g. deg.
Phenanthrene Phenanthrene Saphthalene Naphthalene
Liquid Solid Liquid Solid
2 . 4 2 i0 . 0 3 1.50 i 0 . 0 1 1.87 i 0 . 0 3 1 47 i 0 . 0 1
The values are the average of three measurements.
Discussion ( i ) Undercooling and Cyystallization Velocity in Melts. I n view of the small undercooling for nucleation compared with that expected for clean melts, it is legitimate to conclude that nucleation was heterogeneous. The values of undercooling as given in Fig. 1 are expected to give a comparative idea of the behavior of different mixtures. The results for linear velocity of crystallization are summarized in Fig. 2 where the logarithm of the velocity of crystallization of various melts has been plotted against the logarithm of temperature. Froin the results it is clear that the velocity of crystallization in mixtures falls to much less than a hundredth of the value of the velocity of crystallization of components from pure melts. For the eutectic melt, the crystallization velocity is times the velocity of either of the components. The theory for linear velocity of crystallization in one component has been developed by Frenkel,' Volmer and Marder,8 and quite recently by Hillig and Turnbull. Frenkel's theory for a unicomponent system yields the following expression for the linear velocity of crystallization I when surface diffusion on the crystal is neglected.
Temp. of measurement, OC.
106 45 86 44
B { ACL'4- rT]
I = Ce (3) where B = 1 / 4 a s 2 ( T , / T )(,T , - T ) is undewooling, is the surface tension over the boundary of the crystal embryo, C is a constant which depends on the frequency of encounters of molecules on the crystal boundary, and A.u' is the activation energy of self-diffusion. The activation energy is connected with the viscoshy of the medium. Equation 3 can be easily extended to binary mixtures. When we consider the crystallization of melts of various mixtures of naphthalene and phenanthrene, it is clear that the energy of activation of self-cliffusion, surface tension, and heat of fusion will be of the same order. Hence, the low value of velocity is primarily due to the low value of the constant which depends on the frequency of impacts on the moving boundary. Clearly, the frequency of successful impacts of the separating component in a mixture can never be of the same order as in the melt of a pure component. The frequency of successful impacts would go on decreasing until the eutectic composition is reached. The thermodynamic theory cannot give an estimate of the constant.I0 (7) J. Frenkel, P h y s i k . Z . Sowjetunion, 1, 498 (1932). (8) M. Volmer and M . Marder, 2. physik. Chem., 154, 9;' (1931). (9) W. B. Hillig and D. Turnbull, J . Chem. P h y s . , 24, 914 (1956). (10) H. Reiss, ibid., 18, 840 (1950).
Volume 68, Number 9
September, 1964
R . P. RASTOGIA N D PARMJIT S. BASSI
2404
S o w if the constant is mainly responsible for the low value of the velocity, why is it that the constant far crystallization from eutectic melt is so low compared to that for noneutectic melts? The answer to this question probably lies in the mechanism of eutectic crystallization. I n the case of solidification from noneutectic melts, the crystal boundary moves owing to the impact and subsequent deposition of molecules of the separating phase. On the other hand, in a eutectic melt the separating phase must have a definite ratio of tjhe two components on account of the thermodynamic restrictions. Consequently, only a few encounters would be successful in extending the crystal boundary. I n fact, isolated encounters of individual molecules of one component alone would hardly be of any value. Only when the molecules of both the components in the eutectic ratio strike the boundary would there be a possibility of the growth of the phase. It is evident that this would be a rare event and the value of the constant would be much too low. The above picture of eutectic crystallization has a meaning only when the two phases separate simultaneously. However, it was observed by Bochvarll that piperonal with smaller linear velocity of crystallization was the primary phase in azobenzene-piperonal system. This would lead to pile up of the other component a t the phase boundary leading to the adjoining liquid becoming rich in the second Component. Chaliners and others12 have reported a similar type of observations in eutectic solidification in metals. According to the mechanism proposed by these workers, the eutectic solidification begins with the formation of a nucleus of one of the phases. This would grow until the surrounding liquid becomes rich in the other component and a stage is reached when the second component starts nucleating. Now there are two possibilities. First, the two initial crystals may grow side by side. The second possibility is that there may be alternate nucleation of the two components. The latter possibility fits the observations recorded in the present paper. I t can account for the observation that although the limit of undercooling for naphthalene and phenanthrene and the eutectic are of the same order, the linear velocity of crystallization of the eutectic is much slower than that of the pure components. HOWever, it would be necessary to identify the separating components before this would be acceptable with certainty. Incidentally, our data on linear velocity of crystallization of pure melts satisfy the mechanism as suggested by Hillig and Turnbull according t o which log I = C A T , where I is the linear velocity of crystallization, AT is the undercooling, and C' is a constant involving The Journal of Physical Chemislry
the surface free energy which may or may not be known. According to this mechanism, growth occurs at the sites where the surface is particularly rough on account of lattice imperfections and screw dislodations which intersect the surfaces and produce steps of one or more molecular diameters in height. These steps are the centers of lattice disturbance and hence during growth these steps wind themselves in spirals. For testing the mechanism, log I has been plotted against log AT in Fig. 2 where straight lines are obtained with slopes equal to 2.02 and 2.1 for naphthalene and phenanthrene, respectively. (ii) Microscopic and Microphotographic Studies. The study with a microscope clearly proves that solid immediately separating out from a eutectic melt has entirely different characteristics as compared to the parent components. Further, the opacity of the mixtures is quite evident. These observations appear to be confirmed by the photomicrographs of the solids. Figures 3 and 4 show the crystal aggregate of naphthalene and phenanthrene. The transparency of the aggregates is self-evident. Figures 5 and 6 show dark spots interspersed in the white background. These dark spots are eutectic grains which can be clearly distinguished, The photomicrographs of the solid eutectic matrix is shown in Fig. 7. An extremely regular pattern is evident. The lamellae of different constituents are apparent. Comparison of all these microstructures shows that the crystallization of eutectic has altogether different characteristics as compared to the pure melt. Figure 8 shows that the characteristic of the eutectic is lost after standing when perhaps recrystallization of the eutectic grains takes place. (iii) Heat of Fusion of Solid Eutectic. If H L and H S are the heat contents of the eutectic mixture in the liquid and solid phases, respectively, then the molar heat of fusion (Li)eutectic is simply given by (Lf)eutectic =
HL - H s
(4)
further
HL
=
xjHlL
+ xzHzL + H
M ~
(5)
and
Hs
=
xlHIs
+ xzHzS + H
M ~
(6)
where x1 and x2 are the mole fractions of the two components in the eutectic.and HI and H z are the heat contents of the pure components in the phase indicated by (11) A. A. Bochvar,"Issledovanie mekhanisma i kinetiki kristallieatsii splavov eutekticheskogo tipa," ONTT, 1935. (12) W. C. Winegard, S. Majka, B. M. Thall, and B. Chalmers, Can. J . Chem., 29, 320 (1951).
MECHANISM OF EUT~ECTIC CRYSTALLIZATION
2405
the superscripts L and S. HML and HMS are the heats of mixing in the liquid and solid phases, respectively. If it is supposed that solid eutectic is simply a mechamical mixture, HMSis zero. For such a case
+ x2(HzL - HzS) XI(Lf') + XZ(Lf2) + HML (7)
(Lf)eutect1c = %(HIL- HJS) =
where L f l and L f 2axe the heats of fusion of the components 1 and 2 , respectively. If the picture of the eutectic mixture separating as a mechanical mixture is correct, the experimentally determined heat of fusion per mole should be equal to that given by eq. 7 . The heat of mixing in thle liquid state is not known, but it can be estimated from a thermodynamic analysis of the phase equilibrium da,ta as indicated below. For a regular mixture
R T In y1
= ~ ( X Z ) ~ ;RT
In yz
=
a(xJ2
(8)
where y1 and y2 are the activity coefficients of the two components and a is a constant. The heat of mixing is simply given by
HM
=
~1x2~~
(9)
Kow a can be estimated from a knowledge of the activity coefficients, 'y1 and yz,which can be determined from the expressions
and
where TI0 and T2O are the melting points of the respective components. Thus, from the phase equilibrium data obtained earlier y1 and yz were calculated for different temperatures. Next, In y1 and In yz were plotted against sz2/Tand x12/T. The slope of the best straight line gave Ihe value of a to be 628 joules. Hence the value of heat of mixing is 150 joules. For correctly calculating the heat of fusion of eutectic mixture one must use the values of heat of fusion of the pure components a t the eutectic temperature. To a good approximation, the heat of fusion a t any temperature may be represented by the formula
(Lf')T
=
(Lf')T, - { (Cpl)L - (Cp')') (Tm - T)
(12)
where (Lfl)Tis the heat of fusion of the component i at temperature T, (L:) T, is the heat of fusion of the component i at the temperature T,, (C,l)L is the specific heat of the component i in the liquid phase, and (C,')' is the specific heat of the component i in the solid phase.
From the experimentally determined values of heat capacities, heats of fusion of naphthalene and phenanthrene can be calculated at any temperature when the appropriate value of the heat of fusion of the pure components calculated with the help of eq. 12 is used. ALf, the difference between the experimentally determined value of heat of fusion of the eutectic mixture and that calculated from the mixture law, comes out to be 5800 f 700 joules. Even if a more rigorous formula is used instead of eq. 12, the conclusion would not be affected since ALf would have even greater magnitude. We shall examine whether the value of ALi can be accounted for by the surface free energy of the fine grains of the eutectic mixtures. If ULS is the solid-liquid interfacial energy, the heat content of the solid phase would be given by
HS = xlHIS + X2HzS -
(13)
UL&4
where A is the surface area of the solid phase.
(Lfleutectic = Xl(Lf')
Hence
+ X2(Lf2)+ H M +~ ULSA (14)
If we take ULS = 100 ergs/cm.2, radius of grain = l o p 6 cm., molecular weight of the eutectic mixture = 149.5 g., and density =: 1 g./cc., then ULSA = 4500 joules. This will be the contribution due to the surface energy if the grain size is assumed to be cm. The above considerations show that probably the fact that heat of fusion is greater than that expected from the mixture law is due to the melting of finer grains. Experiments were performed to study the recrystallization behavior optically, the details of which have been described earlier. The possibility of evaporation of the components does not exist since the eutectic solid is put between the two microslides. The intensity of light passing through the slide having the eutectic solid is found to be a function of time showing that the crystal topography changes with time due to recrystallization and rearrangement of the grains. Ax, the difference in the galvanometer reading for the case when the light is allowed to fall on the clean glass slide and the one when the slide contains eutectic mixture, is plotted against time in Fig. 9. Results clearly show that the state of the eutectic changes with time. The transparency appears to increase with time. The reason is obvious. On account of secondary recrystallization, bigger grains tend to be formed with the result that larger areas tend to have a thinner coating of the eutectic mixture.
Mechanism of Eutectic Crystallization We summarize here the characteristics of eutectic crystallization which are revealed by the present study. Volume 68, N u m b e r 9
September. 1964
2406
(1) The linear velocity of crystallization of the eutectic from the eutectic melt is much lower than that for the noneutectic melts. It is 10-6 times the linear velocity of crystallization of pure components from their melts. The magnitudes of undercooling for the eutectic and noneutectic nielts are of the same order. These observations strongly indicate precipitation of mechanically separable phases during eutectic crystallization. (2) The microstructure of solid eutectic as revealed by photographs corresponds to the usual lamellar structure. Photomicrography of the solid eutectic shows no similarity with that for pure components.
The Journal of Physical Chemistru
R. P. RASTOGIA
5.
~ PARMJIT D BASSI
(3) The heat of fusion of the eutectic mixture is greater than that predicted by mixture lam. Part of the excess heat of fusion may be due to the surface energy of finer grains. (4) The characteristics of freshly precipitated eutectic are lost on standing primarily due to recrystallization of fine grains.
Acknowledgment. Thanks are due to Professor A . C. Chatterji for drawing our attention to the problem. P. S. B. is thankful to the Indian Council of Scientific and Industrial Research for financial support.
