Eutexia

George Novello Copley' I . . .

Liverpool College of Technology England I Eutexia

A n intimate tmo-phase mixture consist- ing of 23.6% anhydrous sodium chloride and 76.4% ice melts, under atmospheric pressure, at -21.1C to give a liquid solution of salt in water having the same composition as the initial two-phase mixture. Moreover, a liquid solution of salt in water, of this composition, freezes at -21.1C under atmospheric pressure to give a two-phase mixture of ice and solid salt. To these and related phenomena Frederick Guthrie (1) applied the term "eutexia." He wrote:

ternary system (5) and (b) the line showing the variation of point E (Fig. 2) with temperature, pressure, and composition (6), or as a line a t all points along which the Gihbs free energy of transfer of the two components from the solid state to the solution is zero (7).

It has been said (8) that Guthrie regarded eutectics as definite chemical compounds, but my reading of his papers does not lead me fully to subscribe to this view. Guthrie examined a large number of eutectics in which ice was one of the constitutent solids (9). In

The main argument of the present communication hinges upon his original paper "On Salt Solutions and kttached the existence of oompound bodies, whose chief characteristic is water" he wrote (lo) the lowness of their temperature of fusion. This property of the is clear that if ice and the hydrated or anhydrous salt sepsrstetl bodies may be called Eutexia,* the bodies possessing it eutectic out in DroDortion not combined, but merelv mixetl

with one another, ihe mass would have a constant solibifying- *Used in very much this sense by Aristotle. I should have and melting.point; and this n-ould be below zero to the same

preferred the word hypolytic; but I am instructed that, although amount as would be reached on mixing artificially the anhydrous sanctioned by its use in chemistry, this employment of ' r6 is not or hydrated salt with ice in the same proportion. ~~t when strictly admissible" (1 ) . have distinct and unchangeable relation by weight demanded by

p~ -

bodies or eutecticios (r'rjnrrv). It is a t once apparent that the cryohydrates are essentially eutectic. I t will, however, perhaps be better to make the term more useful by limitingits spplieation. I shall use it, and should like it to be used by others, for bodies made up of two or more constituents, which constituents are in such proportion to one another as to give the resultant compound body a minimum temperature of liquefxtion-that is, a lower temperature of liquefaction than that given by any other proportion. Here, again, the cryohydrates completely satisfy the definition. But i t will be shown that they constitute only one term of a series, that their melting or liquefaction is quite continu- ous with the so-called fusion of mixed metals or salts, and that the eutectic alloys of metals, many of which have been long imper- fectly known, and the eutectic alloys of salts, which I shall describe ($5 207-229), are the perfect homologues of the cryohydrates. Let me, in a word, invite my readers, while looking upon water as fused ice, to trace the analogy between the be- haviour towards solids of water on the one hand, and some other f,..d ".,h.tanm An ,ha -+ha"

the constancy of the solidifying- and melting-point, we have un- doubtedly a numerical physical relation as fixed and no less important than the points of fusion or degrees of solubilities. And if, as I shall show, all the hydrates formed under these conditions have distinct crystalline forms, w-e have all the conditions of chemical association; s t least I know of none other. It is an es- sential element in the existence of these compounds that they can only exist in the solid state below 0-C. Hence I propose to callthemforthe present "cryohydrate~."~ At the ordinary temperatures they melt in their own water of erystallizat,ion and appear as ordinary solutions never saturated. And when once the proportion between the salt and the water in a cryohydrate has been found, the cryohydrate can he formed in any quantity by dissolving the salt in water in the required proportion. Such a solution shows no sign of yielding up ice or anhydrous salt (or other hydrate) until its temperature, on being lowered, reaches a. certain temperature peculiar to %he salt (unless under super- saturation); it then solidifies as a whole, mainti~ining throughout that constant temperature. Above this temperature (that is, in

.-""- ""w""u..ub "- "-- ""-u.,

The majority of textbooks follow G ~ ~ ~ ~ ~ ~ , ~ the melted state) it is precisely in the same predicament, 6s a salt melted in its o m water of crystallization. usage when they say that euteclic means "to melt well" (2 ) or "easv meltincr" IS). but the erroneous o~iuion Guthrie tabulatedz the formulas of twenty-nine . , - ~ . ,

has also been expressed that: " . . . eutectic, derived from the Greek, means "well interwoven" and signifies that a t this concentration the solid which is formed is an intimate mixture of crystals" (4). Used as a noun euteclic means an intimate mixture of two or more kinds of crystals which exhibits eutexia ( I ) , and to be more explicit many authors now speak of this as a eulectic mixture. Euleclic is used very frequently as an adjec- tive, as in eutectic liquid, eutectic composition, eutectic poinl, eutectic temperature, euteclic transformalion, euteclic horizontal, and eutectic reaction isotherm. Euleclic line has been given a t least two meanings: (a) a line in which two liquidus surfaces, each representing a liquid solution saturated with a solid solution, intersect in a

'Present address: Education Ofiees, 14 Sir Thomas Street, Liverpool, 1, England.

596 / Journal of Chemical Education

salts or salt hydrates together with his observations of the temperatures of solidification and the molecular ratios between anhydrous salt and water of their cryohydrates. The latter property of a cryohydrate he called (11) its aquacalent or water-worth and it is clear from his table that it is not always an integer. He also made the following statement (11) about water- worths: It may he perhaps more than accidental that the numbers of molecular water-worths show a distinct tendency to he multiples of 0.5. For my o m part, recognizing the posfiihle range of analytical error, I for the present distinctly farhear to express any

According to Bowden, S. T. (Ref. (S), p. 222), crvohydrale means frost water from the Greek. F. Guthrie also introduced thetermcryogen: "By Cryogen I mean an appliance far obtain- ing a temperature below 0C. I n this paper it always signifier; a freezing-mixture." (Phil. Mag., 141, 49, 206 (1875)).

opinion as to whether we are here dealmg with the same physical force which constitutes a ohemical attraction, and which regulates the integral ratios of molecular combination as most chemists appear to understand the term-%= whether i t is s. distinct or distinctly conditioned force binding the salt and water together in quite a new ratio, or a ratio which can only be brought to the chemical one by multiplication by constants, a t present arbitrary.

Guthrie also wrote the following words concerning eutectic alloys and the geological significance of eutexia: The preconoeived notion that the alloy of minimum temperature of fusion must have its constituents in simple atomic proportion- that it must be a chemical compound-seems to have misled previous investigators. Such misconception could ~carcely have arisen if the existence and properties of the cryohydrates had been known (1s).

We know already, indeed, very many instances in which the mixture of two bodies has a lower melting-point than either of its constituents. Whst must happen then, if a mass of molten rock, such as a silicate, is saturated a t a high temperature with another silicate? When the mixture cools, the second may separate out in the solid form, perhaps as quartz, perhaps as feldspar, or what not. Anon, a t a certain lower temperature, solidification take8 place between the medium and the dissolved rock in dehi te proportion-definite, though perhaps not necessarily in chemical ratio, but presenting that mineralogical ratio which is so striking, and which has not hitherto been satisfactorily explained (IS). I t was also realized quite clearly by Guthrie that enormous pressure would alter the composition of a cryohydrate, for he wrote: Without doubt the cryohydrates would vary in composition if they were formed at enormous pressures; for the variation effected by pressure in the freezing-point of water is not likely to be precisely the same as the variation in the solidifying of a salt out of a solution (14). It seems evident that Frederick Guthrie was not insist- ent in regarding eutectics as solids possessing all the properties of compounds. It is surprising, therefore, that errors in the construction of phase diagrams which originate in the belief that eutectics are compounds should still persist.

Mixtures and Compounds

The study of eutexia affords a splendid opportunity for the reconsideration, from a more advanced stand- point, of the student's earlier learning about mixtures and compounds. There is much evidence that a binary eutectic is a mixture of two crystalline phases and neither a one-phase mixture (solid solution) nor a crystalline compound. The physical and mechanical properties of a mixture of two crystalline phases would be expected to be the average of the corresponding properties of the separate crystals, under the same conditions, weighted according to their proportions in the mixture. The maximum stability of a mixture of solids, at constant temperature (T) and pressure (P), is attained when its Gibbs free energy (F) is a minimum. Since F = E + P V - TS, F is a minimum when its energy (E) and volume (V) are as small as possible and its entropy (Sj is as great as possible. Although the entropy of such a mixture will increase with the comminution of the solids in it, this state will not necessarily be the most stable one, for comminution will also lead to increases in E, and possibly in V , on account of the effects of the shapes, distribution, and surface areas of the two kinds of crystals. For these reasons the simple weighted average result will not he precisely true in practice. Nevertheless, metallurgists

always find that in a binary eutectic-type alloy series hardness, electrical resistivity, density, and other properties vary smoothly, if not linearly, with composition, from the value of the property for one pure crystal to its value for the other (15). Such results show that the alloy of eutectic composition is in no way to be regarded as distinct from any other mixture of its two solid phases under the same conditions.

X-ray crystallography is a means of deciding with certainty whether a solid is a polyphase mixture, a solid solution, or a compound (16). The X-ray method shows beyond doubt that a binary eutectic is a mixture of two kinds of crystals. Although eutectics are usually non-stoichiometric they are not Berthollide compouuds, which are solids containing defect crystal lattices, and not mixtures of solids. Since eutectics are mixtures, it is clear that they cannot be regarded as non-stoichiometric compounds. Thermodynamics of Eutexia

A most important reason for regarding a eutectic as a mixture of solid phases is that it leads to predictions, based upon thermodynamical reasoning, which are in full agreement with the observed equilibrium properties of eutectic systems as well as showing the analogies between these systems and other systems treated by phase theory.

The equilibrium relationships between pressure, temperature, and composition (expressed as a mole fraction) for a binary eutectic system (components A, B) are depicted, in diagrammatic form, in Figure 1 ; A and B are assumed to be completely immiscible in the solid state (Sj and completely miscible in the liquid (F) and gaseous (G) states. I t is possible to have a four- phase equilibrium in this system, comprising solid A (S,), solid B (S,), a liquid solution of A and B (E.), and a gaseous solution of A and B (G.). According to

Figure 1. Binary eutexia. On, OB are the triple points and CA, Cs are the critical points of A and B, respectively.

Gibbs' phase rule such a system must be nullvariant, that is, all its intensive properties are naturally determined and none can be arbitrarily assigned. In particu- lar, the temperature (T,), pressure (P.), and the compositions of the liquid (x&) and gaseous (y&) phases are all naturally fixed for this four-phase equilib-

Volume 36, Number 12, December 1959 / 597

(Constant P, 2 Po)

Figure 2. Iroboris 9ection. mt Ps, of Figure 1.

rium; the line through Go, E. runuing parallel to the composition axis represents this situation in Figure 1. For nearly all eutectic systems the pressure Po, which is the sum of partial pressures of A and B, is extremely small, whereas the pressures at which eutexia is normally considered are a t least one atmosphere. It is therefore customary to look upon eutectic equilibria as condensed systems from which, owing to compression, the gaseous phase is e~cluded.~ The maximum number of co-existent phases for such a condensed system is three, namely S,, S,, and a liquid solution (El; and the variance is unity. The dotted isobaric section of Figure 1 represeuts such an equilibrium for the constant pressure, P,, of the isobar by the line through E parallel to the composition axis. The familiar isobaric section shown dotted in Figure 1 is reproduced, for clarity in subsequent discussion, in Figure 2. Since Pe is normally fixed and equal to the pressure of the atmosphere, TE (euteclic temperature) and X B ~ (eulectic compositia) are also naturally determined. Point E is now termed a eutectie point although Guthrie (17) called it the "point of reflexure."

Three two-phase areas, SAF, SnF, and SASn, are represented in Fignre 2. To these, as well as to similar areas on other phase diagrams, the quantitative phase rule called the tie-line relationship applies and gives information not given by Gibbs' phase rule. In partic- ular, the tie-line rule applies to all mixtures of SA and Sn iucluding the mixture of eutectic composition X B ~ . Because the tie-line relationship concerns only two- phase equilibria it does not apply to the eutectic three- phase line through TEE, and objection must he made to any designation of this line as a tie-line (18). The tie-line rule fails to hold on the eutectic three-phase line in the sense that if the gross composition of such a three-phase system at T,, PE is given, it is not possible to state, without further information, the proportions

For evidence to the contrary see Petrucci, R. H. (Ref.33).) See also the disoussion of euteotic fusion later in this article.

598 / Journal of Chemicol Education

of its three phases; the system is an instance of what Pierre Duhem called an indifferent state (19).

The criterion of constant melting point is neither necessary nor sufficient to characterize a compound. That it is not necessary is shown by the fact that compounds not possessing constant melting points are known: (a) the addition compound formed by benzene and picric acid melts incongruently (meritectically) over a range of about 7C ($0); (b) in ternary systems neither semi-congruently melting nor incongruently melting compounds satisfy the criterion (21). That it is not sufficient is shown by the fact that solid solutions with stationary melting points have this property (22). Hence the constant melting point of a eutectic neither proves nor disproves that it is a compound. It remains of interest to compare the fusion of a binary eutectic with the fusion of a binary compound. The following processes, reading from left to right, all occur, at constant temperature and pressure, with increases in enthalpy and in entropy and represent indifferent states:

(i) congruent melting: S, = F (ii) meritectie melting: S, = S2 + F (iii) eutectic melting: 8, + S2 - F

In (i), (ii), and (iii) S may represent solid solution in- stead of pure solid; in this case (i) represents a stationary melting solid solution, (ii) represents peritectic melting, while (iii) still represents eutectic melting and indeed, it is this kind of eutectic, involving solid solutions, that is most commonly encountered in practice. Figure 3, which should be cornparedwith Figure 2, shows the isobaric condensed phase diagram of a binary eutectic system involving solid solutions (S,, SI). Schemes (i), (ii), and (iii) also show that eutectic melting is more akin to meritectic and peritectic melting than t o congruent melting, in that melting of types (ii) and (iii) both involve two solid and one liquid phase in a binary system. On phase diagrams this analogy is

Figure 3. Binary eutectic system with solid rolvtionr Sir SI. Cornpore with Figure 2.

represented by eutectic, meritectic, and peritectic three-phase lines. These are not the only three-phase equilibria possible in binary systems: F. N. Rhines (83) has listed twenty-six types of such equilibria, of which his type c is depicted on the front isothermal section of Figure 1, on which a line parallel to the composition axis represents the equilibrium between solids SA, SB, and a gas of composition represented by point 7. An important type of three-phase equilibrium encountered in binary alloy systems involves three solid solutions (81 + S2 = S3); because of its close analogy to (iii) it is said to be eutectoid.

The possible equilibria between two immiscible solids, A and B, and a liquid solution of A and B, have been studied in terms of the intensive variables temperature (T), molar Gibbs free energy (F) , and mole fraction (xH) (84). The molar Gibbs free energy of an ideal solution is

where F;, F; are the constant molar Gibbs free energies of the pure liquids A and B a t the temperature and pressure of the solution. Function (1) has the form shown in Figure 4 and has the property that the tangent to the curve at X makes intercepts on the A and B axes (xB = 0 and 1, respectively) equal to FA and FB (84).

( I ; P constant ) I

Figure 4. Gibbs free energie. of solutions of A and B

According to Gibbs' phase rule a binary system existing in one phase (the liquid solution) has a variance of three, so that a system represented by X (Fig. 4) is completely determined, apart from its amount, by the temperature and pressure of the diagram and by either the value of XB or F for the solution. If the solution be in equilibrium with SA, say, then the variance be- comes two, and there can be only one point X (Fig. 4) for which this is possible. This point on the curve is found by drawing the tangent to the curve from the point (FAS, XB = O), where FAS is the molar Gibbs free energy of SA at the temperature and pressure of the

Figure 5. Isobaric d i o g r m of F-T-XB relations in o binary eutectic syrtem.

diagram. Let the pressure from hence be assumed to be fixed and let the temperature T for Figure 4 be considered in relation to the melting points (TAP TB) of A and B a t this fixed pressure. (i) If T > T., > TB, then FAS > F k and FBS > F;, and no tangents can be drawn from points (FAS, XB = 0) and (FBS, x,, = 1) to the curve (Fig. 4). In these circumstances the liquid phase is always unsaturated at all compositions and is represented by the area above TA in Figure 2. (ii) Similarly, if TA > T > TB, only one tangent, that from (FAs, 0) can be drawn to the curvc and the solution is saturated with SA. This situation is rep1,esmted by an area between parallels to the composition axis through TA and TB in Figure 2. (iii) If TA > T, > T, tangents can be drawn from both (FAS, 0) and (FgS, 1) to the curve. This situation is represented by areas between the lines parallel to the composition axis through TB and TE in Figure 2. When the two tangeuts coincide, SA and SH will be in equilibrium with one another and this is the interpretation of the eutectic phenomenon. At temperatures lower than TE the line joining (FAS, 0) and (FsB, 1) lies below the solution curve, corresponding to the fact that mixtures of SA and S, are more stable than any systems involving solutions. This situation is represented, in Figure 2, by the whole of the area below the eutectic three-phase line.

Some of the results which have just been discussed are depicted in Figure 5. Departure of the solution of A and B from ideality does not materially alter the foregoing conclusions unless it leads to partial miscibility in the liquid state. Partial miscibility in the solid state gives rise to Figure 3, the F - x diagram, at T, and PE, for this case is given in Figure 6 which represents the equilibrium of the eutectic liquid (FE) with eutectic solid solutions (S,E, S9E).

For the case in which the liquid phase is an ideal solutior~ and the solids A and B are immiscible it is possible to calculate, with the help of thermodynamics, values for T, and xBE (85).

Since a binary three-phase system such as a condensed eutectic system is univariant, it follows that there must exist unique relations between any two of its intensive properties. The more important of these

Volume 36, Number 12, December 1359 / 599

Figure 6. Gibbr free energies of liquid and solid solutionr or functions of composition a t the evtectic temperature and pressure.

relations are between (a) the eutectic temperature and pressure and (b) the eutectic composition and pressure. Relation (a) has the familiar form of the Clapeyron- Clausius equation,

which is usually only considered in connection with univariant two-phase equilibria in unary systems. It is not difficult to show that relation (a) is (86)

Equations (2) and (3) enable a comparison to be made between melting, a t constant temperature and pressure, in the case of (2) a pure solid (pis then the solid phase and a is the liquid phase) and (ii) a eutectic mixture of two pure solids. Equation (2) makes it clear that the transformation concerned is that of one mole of solid into liquid, whereas equation (3) makes it equally clear that the corresponding transformation is that of one mole of a mixture of two solids A and B to give a liquid solution of the same composition. Thus, although equations (2) and (3) are both Clapeyron- Clausius equations applying to univariant equilibria, they refer to physically distinct processes.

Relation (b) can be shown to be (26)

and it can also be shown (26) that the sign of this expres- sion is that of the difference in the final bracket. The effect of pressure on the melting point,s of t,he compo-

nents and on the eutectic temperature and composition for the system urethan-diphenylamine are given in the table. This table (27), which illustrates (3) and (4), shows that although T,, like the melting-point of a pure solid, is a function of pressure, a eutectic differs from a compound in that its composition also varies with pressure.

Variation, with Pressure, of Eutectic Temperature and Composition (27)

Melting-point/'C -Eutectic- Pressore/ Diph~nyl- zx kg cm-a Urethan amme TE/'C urethan

Microstructures of Eutectic Alloys

The temperature-composition diagram, a t atmospheric pressure, of the bismuth-cadmium system, is given in Figure 7. It will be assumed that an alloy of bismuth and cadmium is cooled quasi-statically, a t constant gross composition, red = 0.3, from about 350C. The primary solid phase that separates, starting a t about 250C and continuing until T, = 144C is reached, is bismuth, while a t T , solid bismuth and solid cadmium separate in the proportions present in the eutectic liquid (xcg = 0.55). When complete solidification has occurred, the proportion of primary solid bismuth to eutectic alloy is given by applying the tie-line rule to the Bi(S)F two-phase area just above T,, while the proportion of bismuth to cadmium in the solid alloy is given by applying the tie-line rule to the Bi(S) Cd(S) two-phase area just below T,. The metallurgist is usually more interested in the former result, which he refers to as the determination of the proportions of the constitutents, than he is in the latter result, which is the determination of the proportions

Figure 7. lraboris evtectic phme diogram of the bismuth-cadmium system.

600 / Journal o f Chemical Education

of the phases. The term constituent is used by metal- lographers to signify " . . . a characteristic and recogniz- able structure which can be identified as a unit in micro- scopic examination of a given material, and which serves as a structural unit in determining the properties of that material. A constituent must be carefully distinguished from a phase or a component of the alloy (28)." In eutectic alloy systems the eutectic constituent is a crystalline structure of eutectic composition. It is often found convenient to draw a dotted line (ef) from the eutectic point e parallel to the temperature axis in the phase diagram (Fig. 7) to indicate the composition of the eutectic constituent, but it is quite erroneous, as is done in some textbooks, to draw this as a full line in the manner that the solidus Tsi efee"Tcd, the liquidus TsieTcd, the solvns4 e'f', and the solvus eYf" are drawn in Figure 7. Solidus, liquidus, and solvus and similar curves on phase diagrams are boundaries of two-phase areas in binary systems; ef is not such a line. If it were, it would imply that four phases, Bi(S), Cd(S), and solid and liquid of eutectic composition could partake in the eutectic equilibrium, so that, contrary to what is observed, the eutectic temperature and composition could not be varied by changing the pressure, for such a system would be nullvariant.

When removal of heat takes place a t T,, the eutectic liquid is converted into the eutectic constituent by the simultaneous deposition of the two solids with which it is in equilibrium. For this reason, the eutectic constituent is often a fine and intimate mixture of two types of crystals and usually possesses, if an alloy, great strength aud impact resistance. Nevertheless, there is not one unique structure that can be regarded as characteristic of all eutectic constituents. One obvious reason why this should be so is that the relative proportions of the two solid phases in a eutectic constituent vary widely; thus, the antimony-lead eutectic has xpbP = 0.80, whereas the beryllium-silicon eutectic has xsi' = 0.32. An extreme case is found in the tim- silicon system where the eutectic composition is so near to that of pure tin as to elude identification; in these circumstances the system is referred to as monote~tic.~ The structures of a variety of binary eutectic constituents as revealed by polishing, etching, and micropho- tograph~ are readily available (39).

X-ray examination of certain eutectics showed that the particles of the two phases precipitated so that they were favorably oriented with respect to each other (30). The interfaces between the particles of the two solids were arranged so as to give the easiest alignment of the crystal planes of one phase with those of the other. It is considered that the solidification of a eutectic alloy is a process of much greater complexity than that of a

metal (31). The fine structure of the eutectic constituent usually

observed re~resents a condition of relativelv h i ~ h sur- "

face energy, but not necessarily, on account of the de- gree of order of the structure, of relatively high entropy. In consequence it may be unstable with respect to a mixture of the same composition which has lover surface energy and a more disordered structure. By keeping a

Thisconvenient termis so used by Rhines. (Ref. (IS), p. 34.) The term monotectic is also used to describe a binary three-

phase reaction in which a liquid phase loses heat to yield another liquid phase and a solid phase. (Ref. (la), p. 72).

eutectic alloy just below T, for a long period, growth of its small crystal grains into larger aggregates occurs and the typical appearance of the eutectic constituent is thereby destroyed. Such eutectics are said to be divorced and can be formed during the freezing of eutectic alloys if the rate of removal of heat is slow enough, as well as in the annealing of alloys subsequent to solidification.

The melting of eutectic alloys is related to their formation by crystallization; in fact, the first stage of fusion, and the last stage of freezing, of a eutectic alloy is always the fusion or freezing, a t t,he eut,ectic temperature, of the eutectic constituent. The mechanism by which the solids in a eutectic constituent melt to give the eutectic liquid as soon as the eutectic temperature is reached has been raised by N. 0. Smith (52) and discussed further by R. H. Petrucci (33). Professor Petrucci considers that the process takes place via the vapor phase, albeit the vapor pressures (or the partial vapor pressures in air a t one atmosphere pressure) involved may be extremely low. Yet it will be evident from the account I have given of the thermodynamics of eutexia that two solid phases present together in a mixture should, on being heated a t T, and at some pressure high enough to prevent the appearance of vapor (if necessary by using a special cylinder and piston), melt to give eutectic liquid. I think that in this lies the difficulty which was raised by Smith when he wrote (33): "Why should an intimate mixture of A and B begin to melt a t a temperature lover than the melting point of both pure compounds, even when their volatility is negligible?"

Anart from the work cited bv Petrucci i33). I have -- A~ ~~ - ~ , . . been unable to trace any reference to studies of the mechanism of eutectic fusion, but studies have been made of the analogous eutect,oid transformation, ex- emplified by

ferrite + cementite = austenite in the iron-carbon system. The eukctoid transforlwa- tion, S1S2 (S3), is univariant, like the eutectic transformation SIX2 (F),6 under ordinary conditions, since both involve a binary system of three phases. The inclusion of either a liquid or a gaseous phase mould make the eutectoid system nullvariant and this new phase might be invoked in understanding the mechanism of the SISz (Ss) transition if Petrucci's lead is followed. Rut neither of these possibilities seems to have been so used in the case of iron-carbon eutectoid t~ransformat~ion. On the other hand, it appears that the interact,ion of a solid solution of carbon in body-centered cubic iron (ferrite) with the compound of formula Fe3C (cementite) to give a solid solution of carbonin face-centered cubic iron (austenite) is essentially a process of interstitial diffusion of carbon atoms (34). I t therefore seems to be a possibility that eutectic fusion is also capable of interpretation as a diffusion process, interstitial or otherwise.

Summary

An account has been presented of the reasons why a binary eutectic must be regarded as a two-phase mix-

' Recently recommended notation for phase transitions

Volume 36, Number 12, December 1 9 5 9 / 601

ture of solids and not as a Daltonide or Berthollide compound. At the same time it has been emphasized that this two-phase eutectic mixture is a structurally important constituent of many metallic alloys. The correct representation of these relationships in phase diagrams has been discussed. It is clear that similar ideas apply to higher order eutectic system^.^ Acknowledgments

I am grateful for the help I have received in the preparation of this paper from correspondence with Professor K. J. Mysels, Professor R. H. Petrucci, Dr. N. 0. Smith, and Dr. A. F. Wells. Raif Copley kindly drew the diagrams. ' Guthrie (Ref. (I), p. 465) used the terms bi-, tri-, and tetr*

eutectic allovs where the terms binarv. ternarv. and ouaternsrv ". " . eutectic alloy are now used; he also envisaged higher order eutexia (Ref. (I:, p. 468). Literature Cited (1) GUTRRIE, F., Phil. Mag., 151, 17, 462 (1884). (2) GUGGENHEIM, E. A,, Trans. Faraday Soc., 51, 876 (1955). (3) BOWDEN, S. T., "The Phase Rule and Phase Reactions,"

Mctcmillan & Co., Ltd., London, 1938, p. 149. (4) PRIGOGINE, I., AND DEFAY, R., "Chemical Thermodynam-

ics," translated by EVERETT, D. H., Longmans, Green & Co., Ltd., London, 1954, p. 178.

(5) EPSTEIN, P. S., "TextbookoiTherm~dynamic~," John Wiley & Sons, Inc., New York, 1937, p. 196.

(6) ZERNIEE, J., "Chemical Phase Theory," Ae. E. Kluwer, Deventer, The Netherlands, 1958, p. 76.

(7) PRIGOGINE AND DEFAY, op. eit., p. 364. (8) FINDLAY, A., CAMPBELL, A. N., and SMITH, N. O., "The

Phase Rule and its Applioations," Dover Publications, Inc., New York, 1951, p. 140.

(9) GUTHRIE, F., Phil. Mag., [5], 6, 105 (1878). (10) Ibid., 141, 49, 1 (1875).

Ibid.. 141 49. 214 (1875) lbid.; i5j, ii, 468'(188i). Ibid., [4], 49, 20 (1875). Ibid., [5], 1, 450 (1876). S ~ T H , M. C., "Alloy Series in Physical Metallurgy,"

Harper & Brothers, New York, 1956, p. 63. BIJYOET, 3. M., KOLKMEYER, N. H., AND MACGILLAVRY,

C. H., "X-ray Analysisof Crystals,"translated by FURTH, H. L.. Butterworths Scientific Publications. London. 1951, p. 47.

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