A CRITICAL STUDY OF SOME IRON-RICH IRON-SILICON ALLOYS CHU-PHAY YAP’ Department of Chemistry, Washington Square College, New York University, N e w York City
Received February 21, I933
On account of the technical importance of the iron-silicon alloys, considerable work has been done in recent years (1) on the constitution diagram of the system. Of particular importance both from the standpoint of the purity of the alloys used and the thoroughness of the investigation, is the work of Haughton and Becker, while the earlier work of Phragmen is also noteworthy. It appears that only the compound FeSi is accepted beyond dispute, while there is some doubt regarding the compounds FeaSiz and FeSiz (or FezSis). The existence of a compound corresponding to FeaSi has been advanced by Corson; and Stoughton and Greiner, in their critical review of the literature and from their resistance study, also support Corson’s view. On the other hand, Haughton and Becker, Phragmen, Murakami, and others deny the existence of FeaSi. Phragmen claims it to be merely a distinguished point in the series of solid solution, particularly because he found the limit of solubility to be 15.4 per cent silicon, as obtained, however, by extrapolation of the x-ray data. In all the work done so far, each investigator appeared to be merely preoccupied with the interpretation of his results from a purely physical point of view, neglecting altogether considerations which would have been arrived a t from a chemical standpoint. It is the writer’s specific purpose to bring certain thermodynamic considerations to bear in the interpretation of his results as well as the results of other investigators. Hence, emphasis in this paper will be on chemical and not physical methods. The writer has been particularly fortunate to have obtained through the kindness of Mr. K. Marsh of the Engineering Foundation Monograph Series, five samples of extremely pure iron-silicon alloys prepared in the Union Carbon and Carbide Research Laboratories, Inc. Some ordinary commercial iron-silicon alloys were also obtained from the Duriron Co., Dayton, Ohio. The composition of the alloys is given in table 1. It will be seen that the composition of the pure alloys in which the writer is mainly 1 Present address: Research Institute of Physics and Chemistry, Directorate of Ordnance, Nanking, China. 95 1
952
CHU-PHAY TAP
interested lies very close to that of FesSi. The samples were received in the “as cast” condition and so they were annealed at about 900°C. for 150 hours in order to insure real equilibrium. TABLE 1 Composition of the iron-silicon alloys ~
NO.
PER CENT SI
~1 2 3 4
PER CENT Si BY ANALYSIS
NO.
PER CENT
12.39 13.11 13.99 14.50
5 6* 7* 8*
17.0 5.0 25.0 32.0
13.0 14.0 14.5 15.0
FIG. 1. APPARATUSFOR
THE
Si
PER CENT Si B Y ANALYSIS
15.56 4 92 Not analyzed Not analyzed
DETERMINATION OF THE THERMOELECTRIC ALLOYS
CHARACTERISTICS OF IRON-SILICON
THERMOELECTRIC CHARACTERISTICS
Corson (1) made a study of the change in the resistivity of the ironsilicon alloys with respect to the silicon content, but on account of the fact that he used specimens which were not sufficiently annealed to obtain real equilibrium, doubt has been cast on this phase of his work. It is well known that the true value of the resistance of alloys is very difficult to measure except in the form of a wire, but from a study of Corson’s paper the writer is convinced that no systematic error can account for the very sharp cusp at the composition corresponding to Fe3Si. As a general rule, the resistance curve is parallel, if not congruent,with the thermoelectric curve, and since the thermoelectric characteristics can be studied much more accurately, the writer adopted this method to ascertain if a similar cusp could be found. As the specimens were only 2 to 6 cm. in length and about 1.5 cm. in radius, a special but simple apparatus had to be constructed as shown in figure 1. The thermal E.M.F. was read
STUDY OF IRON-RICH IRON-SILICON ALLOYS
953
against pure nickel at 75°C. and 50°C. at the hot junction and a t 0°C. at the cold junction. After considerable trial, we found that by stirring the mushy mixture of pulverized ice in water a t a speed of 1500 r.p.m., while the hot water was stirred at a speed of only 500r.p.m., strictly reproducible results could be obtained. The millivoltmeter used was calibrated against a standard cell on the Type K (Leeds and Northrup) potentiometer. The results of this study are shown in figure 2. 2.2
1.1 180
2 0
0.9
.a d 4
0.8
I e 0
0.7
9 .f 0.6 L +3
0
H
0.5
0
E
al
f
0.4
0.3 0.2
u 1 J m Per cent Silicon FIQ. 2. THE THERMOELECTRIC CHARACTERISTICS OF SOME RON-SILICON AQAINST NICKEL The temperature coefficient (a)is also given
ALLOYS
The sharp cusp in the resistivity-composition curve obtained by Corson is thus confirmed in figure 2, and since the composition of the alloys used by the writer varied by only small increments, the cusp may be placed with some certainty a t exactly 14.35 per cent silicon, corresponding to the compound FeaSi. As Corson properly pointed out, the resistivity-composition curve he obtained is characteristic of a binary system of two metallic components forming a continuous series of solid solutions, either or both of
954
CHU-PHAY YAP
which components may also be a truly intermetallic compound. Hence, if the alloy corresponding to the composition of.,3Fe/Si were only a distinguished solid solution, the resistivity-composition curve should reasonably be expected merely to vary continuously from the resistivity of pure iron to that of 3Fe/Si without passing through a maximum, as was obtained by Corson. If we consider a truly metallic compound as one that is characterized by low resistivity, then FesSi (hereafter designated as + for convenience) is a metallic compound of the shared electron type, i.e., a nonpolar compound. T H E ELECTRODE POTENTIAL O F IRON-SILICON ALLOYS
The electrode potentials of alloys are very significant characteristics of their condition in the heterogeneous systems, i.e., whether compounds or solid solutions are formed. Suppose we have a cell with pure iron as one electrode and an iron-silicon alloy as the other electrode, both being immersed in the same sdution of electrolyte (such as ferrous sulfate); then when a current passes through the cell, a certain quantity of iron is transferred from the pure iron electrode to the alloy electrode, thus Fe(pure) = Fe(in solid solution); AF = RT In a‘ = -NEF
Hence, E
=
- ( R T / N F ) In a’ =
-k
In a’
(1)
when the activity of pure iron is taken as unity and a’ represents the activity of iron in the solid solution. It is noteworthy that the electrode potential in equation l is independent of the nature and concentration of the electrolyte used, provided N is the same. In the case of an intermetallic compound acting as an electrode, the problem becomes much more complicated, as we no longer have an essentially ionic transfer following the Faraday law of electrolysis. This is due to the fact that intermetallic compounds, as a rule, are not of the polar type. The electrode potentials thus obtained may be meaningless, in regard to their thermodynamic significance, being perhaps nothing better than the polarization potentials. Nevertheless, even the polarization potential is also characteristic of the compound and that compound alone, and is, therefore, significant in revealing the presence of a particular compound. I n figure 3 is shown the experimental set-up for the determination of the electrode potential of the iron-silicon alloys against pure iron. The electrolytic hydrogen was first purified in a pyrogallic acid train, then in a platinized asbestos train, heated to about 500°C., and then bubbled through the boiling distilled water in the flask A, the stirring helping to rid the water of any dissolved gases on account of their mutual solubility (Le., providing
STUDY OF IRON-RICH IRON-SILICON
ALLOYS
955
a gas-gas interface). After the water had been boiled for thirty to fortyfive minutes, a cooling vessel was introduced under the flask. When the water had reached room temperature, the measuring bulb B was evacuated by a pump, and water was allowed to flow in from the reservoir flask A. This operation was repeated, so that the second time we were more certain that the bulb B contained only gas-free water. The requisite amount of the FeS04.7H20salt to make a N/10 solution was placed in the cellchamber C and the electrodes introduced as shown in figure 3. The cell chamber was then evacuated and hydrogen allowed to flow in. Stopcocks Nos. 2 and 3 were then opened, so that the flowing hydrogen could force the water from the measuring bulb B into the cell chamber C. During the course of the run, hydrogen was bubbled through the solution at the rate of a bubble per second. The potential was measured on a Type K potentiometer.
FIG. 3. APPARATUSFOR THE DETERMINATION OF THE ELECTRODE POTENTIAL OF IRON-SILICONALLOYSAGAINST PUREIRON
The electrolytic iron electrode was kindly prepared for the writer by Mr. T. S. Fuller of the General Electric Research Laboratory. It had been previously remelted twice under very high vacuum. The ends of the electrodes were polished in the same manner as for metallographic examination. It was found that without proper etching, the cell did not come to equilibrium for as long as two weeks. After many trials, it was finally decided to use the ordinary HF-HN03-glycerine etchant as well as aqua regia. The latter drastic treatment was found necessary in order to remove the effect of cold-working during the process of polishing. I n order to remove any surface inequalities due to preferential dissolution, all alloys were again repolished lightly and etched with a weakersolution of HF-HN03glycerine. The electrodes, with the exception of the polished surface, were given a smooth coating of paraffin.
956
CHU-PHAY YAP
A few words may be said regarding the process of recrystallization of the FeS04.7Hz0 salt, as it is very difficult to keep in a reduced state. I n the preliminary part of the work, considerable trouble with oxidation of the ferrous salt solution was encountered, but when the recrystallized salt was later used, the trouble disappeared altogether. Baker’s ordinary c. P. brand of the salt was dissolved in freshly distilled water to form a saturated volt 0.35
0.36
13.99 Per cent
* hStiCally
0.25
S i l k o n Alloy etchad i n boiling
y u regia
+ Lightly etched In HF-HN03-Glycerine 0.20
0.15
0.10
0.05
0 .oo 0
10
20
FIG. 4. THE CHANGEI N
30 THE
Hours
40
!a
€4
70
eo
ELECTRODE POTENTIAL OF AN IROX-IRON-SILICON
ALLOY WITH RESPECTTO TIMN Note that the equilibrium is approached from both sides
solution. Then 95 per cent alcohol saturated with paraffin was added to precipitate the hydrate, FeS04.7H20.2 The salt was collected and allowed t o dry on porous porcelain and then kept in a bottle covered with black paper. I n this way, on account of the adsorption of the paraffin on the surface of the salt, the ferrous salt was well protected from oxidation for a long time. *The salt was merely assumed to be the heptahydrate; no actual analysis was made.
STUDY OF IRON-RICH IRON-SILICON ALLOYS
957
In figure 4 is shown a typical example of how an iron-silicon electrode comes to an equilibrium in the cell. The upper curve is that due to the alloy electrode that was etched in boiling aqua regia, while the lower curve is that due to the alloy that was etched less drastically with the HF-HN03glycerine etchant. While the upper curve suggests polarization phenomena, the lower curve proves that this is not the case. The fact that equilibrium is approached from both sides indicates that the cell is apparently reversible. I n the absence of other pertinent thermal data (e.g., entropy, heat of formation, etc.), we are unable at present to interpret the actual significance of
Th r 0.729
-r v= 0.395 I
VOI'
0.1
0.1!
::::b f =0.1194
0 10
20
Jo Per cent Si
FIG.5. THE ELECTRODD POTENTIAL OF SOMEIRON-SILICON ALLOYB the electrode potential, although the activity of iron can be direct'ly calculated from equation 1. I n the range up to 5 per cent silicon (by weight) the electrode potentials are very small, so that the influence of impurities and surface conditions becomes marked; no attempt was therefore made to measure E nor dE/dT. Although theoretically the electrode potential of the 13.99 per cent silicon alloy should be much less than that of the compound 6,the observed potential is, however, that of the compound as shown in figure 5. This may be attributable to the fact that after long annealing a t high temperatures,
958
CHU-PHAY YAP
there must have been some tendency (present in all solid solutions) towards unmixing of the components in solution-in this case, apparently to iron and 4. If the solute were silicon, we would hardly have obtained the potential characteristic of 4. This suggests that the electrode potential method of determining the phase structure in an alloy is very sensitive. The existence of B compound Fe3Siz (7) is also confirmed. That the compound is a result of a peritectoid reaction ‘‘4 E e 7” is shown in a very interesting way as follows: a commercial 25 per cent silicon alloy showed a potential of about 0.725 volts in the “as cast” condition, indicating the presence of E, but another sample in the annealed condition showed a potential of about 0.395 volts, which is the potential characteristic of q. It also appears from this observation that q does not form solid solutions with other impurities found in the commerical alloys and that the composition appears to be constant. The electrode potential of E is about 0.725 to 0.729 volts, considerably higher than that of 7.
+
MICROSCOPIC EXAMINATION O F THE ALLOYS
For the purpose of correlating the results, a microscopic examination of the alloys was made. It is quite true, as Corson pointed out, that no metallographic evidence has ever been produced proving conclusively the existence of the compound q. In the hope that the compound 7 might not belong to the isometric system, the writer used a polarizing microscope (Reichert make) in an attempt to detect its presence in the 15.56 per cent silicon alloy, but no positive confirmation could be obtained. In the case of the 13.99 per cent silicon alloy, the electrode potential indicates the presence of some 4 and so the alloy was studied intensively to ascertain if 4 can be distinguished from the ordinary solid solution. An attempt to study the inner symmetry of 4 by means of etch figures failed, because even boiling aqua regia did not yield etch figures. The specimen was then placed in a ferrous sulfate solution and allowed to oxidize in the air for about one month. This resulted in the production of some etch figures (square and rectangular pits), but they were located in places where their position could not be correlated with respect to the large grain^.^ It should be noted here, however, that the microscopic evidence presented by Corson regarding the existence of 4 is highly questionable in value. The “bushings” he observed were probably due to strains produced either in the process of cooling from the melt or during the polishing operation of the metallographic samples. 8 It was hoped that if segregation of @ had appreciably taken place within a large grain, the etch figures in one part of the grain might differ in orientation andshape from those in other parts of the grain where @ is localized, The only indirect evidence of @ in the sample lies in the fact that certain grains (rather small and located within a large grain) were apparently unattacked by any chemical reagent, however drastic the treatment.
STUDY OF IRON-RICH IRON-SILICON
ALLOYS
959
X-RAY ANALYSIS O F THE ALLOYS
Although Phragmen had made a careful x-ray analysis of the iron-silicon alloys he prepared, he did not use as pure alloys as the present writer has under investigation. The alloys, although already annealed for 150 hours a t 900°C., were given another 150 hour annealing a t the same temperature and cooled down to room temperature in 24 hours in order to determine whether a hyperstructure might be formed in the alloys with less than 14.35 per cent silicon, as a result of further unmixing of the components in solid solution. Although the accuracy of the x-ray measurements on films taken with the ordinary cassettes that com? with the General Electric Go. apparatus is only of the order of f0.005A., the absolute error can be minimized as follows: If we use as a standard for comparison pure iron, whose lattice parameter is known accurately, then as the effect of silicon is merely to shift the diffraction lines, the absolute length of any diffraction line from zero beam can be calibrated each time against the known (calculated) length of the corresponding line for pure iron. In this way, irrespective of the shrinkage of the film (which is about 12 in. long) or slight inaccuracies of the cassettes used, the absolute error is thus reduced to about =tO.OOl&. As a result of several sets of measurements, the lattice partmeter of the electrolytic iron used by the writer was determined to be 2.8608. The films were measured on a small “home-made” comparator accurate to about 0.002 cm. The results of the present investigation are graphically shown in figure 6 in comparison with those obtained by Phragmen. According to him, an alloy of the composition 3Fe/Si is merely a distinguished point in a series of solid solutions. The fact, however, that the lattice parameter of 4 obtained by the writer is the same as that found by Phragmen, while in the range of solid solutions appreciable differences occur, is cogent argument in support of the assumption that 4 is a compound. According to figure 6, the limit of solid solution is exactly that represented by 4. The difference in our results may be explained as follows: As unmixing takes place, the solid solution decreases in concentration with respect to silicon, hence, the fundamental lattice constant of the solid solution should increase accordi n g l ~ . We ~ should, therefore, expect the diffraction lines of both the solid solution and 4 to be present, but this was not the case. It should be
* Since this work was completed, the writer has been able t o increase greatly the accuracy of the G. E. cassette b y a special device, onwhichapatentisbeing obtained. The pure alloys were unfortunately spoiled in the course of some other experiments. However, the 5 per cent silicon coommercialalloy was again analyzed and was found to have a lattice constant of 2.8562A . based on pure sodium chloride.
960
CHU-PHAY YAP
pointed out that the x-ray method is rather insensitive for the detection of small amounts of a second phase. VC’ith the composition represented by 3Fe/Si, it appears reasonable to assume with Phragmen that if we take twice the size of the unit cell of iron and distribute the silicon atoms at the corners and face-centered positions, we have what corresponcs to the hyperstructure of 4, with a fundamental lattice constant of 5.6308. On a film taken with a rotating Debye-Scherrer type of camera, the only additional line determined with some certainty was 311, although even mere faint traces were also found which could be ascribed to the 2 (100) and 2 (111)planes. Although this is thus a confirmation of the regular distribution suggested by Phragmen, the x-ray method
R r cent
FIG.6. THE CHANGE IK
THE
Silicon
- BY
weight
SIZE OF THE UNIT CELLWITK RESPECT TO SILICOK CONTENT
cannot by itself determine whether C$is a solid solution or a compound, as it does not describe the force-field between the different atoms in the lattice. THERMODYNAMIC CONSIDERATIONS O F THE EQUILIBRIA
A critical study of the original papers by Tammann, Kurnakow, Gontermann, Sanfourche, el al., reveals that their results can be consistently interpreted as showing a “singular point” in the liquidus-solidus curves at about 14.4 per cent silicon, although according to Haughton and Becker, the singular point is about 12.2 per cent silicon. If the singular point were at 14.35 per cent, then the phase diagram of the iron-silicon system could be easily represented as a composite of the following binary systems: Fe-FeaSi, FesSi-FeSi, FeSi-FeSi,, and FeSiz-Si. In such a case, the phase rule itself
STUDY O F IRON-RICH IRON-SILICON
ALLOYS
961
justifies us, even in the absence of any kind of independent evidence, in treating FeaSi as a compound. It can be shown from thermodynamics that in heterogeneous equilibria involving the melt and a solid that is a solid solution (2)
in which a is the activity of A in the melt and a’ its activity in the solid solution. When we substitute mole-fractions for activities, equation 2 reduces to d In(N’/N)A d (l/T)
AHA
=-
R
(3)
so that if we plot In (N’/N) against 1/T, the slope of the curve as ( N ’ ~ NA) 1 should give us the correct value of A H A , the heat of fusion of the pure solvent at its melting point. We are here required to make some a priori assumption regarding the nature of the solute, when the solvent alone is a pure and simple substance, like iron. In figure 7, curve I is calculated on the assumption that the solute is in the form of silicon atoms. We know from thermodynamic considerations that a positive deviation from Raoult’s law is normally associated with an absorption of heat and an expansion in volume, and a negative deviation is accompanied with the opposite effects; the former also indicates a tendency towards unmixing, while the latter indicates a tendency towards the formation of compounds (3). As ideal solutions are defined from the standpoint of Raoult’s law, any deviation from Raoult’s law will be indicated by the deviation from the ideal solubility curve.5 We note that curve I shows a large negative deviation, which thus indicates that the solute forms a compound with the solvent atoms. Hence, curve I1 is calculated on the assumption that the solute is FesSi, which is also evidently incorrect, as it gives 108.5 calories per gram as the heat of fusion of pure iron. We note, however, that curve I1 is linear for some range of temperature and concentration, and this constant deviation indicates a definite change in the ratio of molar concentrations, or, what is equivalent to it, a change in the total moles taking part in the equilibria. If we thus assume the solute to be (FesSi)~,~ then we obtain curve 111,which In a strict sense, when solid solutions are involved in the equilibrium with the melt, the term “ideal solubility curve” is meaningless, as each solute will have a characteristic distribution constant. It is indeed curious-perhaps entirely accidental-that all compounds in t h e iron-silicon system can be represented by FeeSi,, where n is an even number. It inay be recalled that silicon, like GeGe, GeAs, ZnSe, ZnS and CC (diamond) is of the covalent type and may be considered diatomic. I n view of this fact, the assignment of the formula (FeaSi)zor Fe& becomes reasonable, T H E JOURNAL OF PHYSICAL CREJIISTRY, VOL. XXXVIk, NO.
7
962
CHU-PHAY YAP
gives the correct heat of fusion of iron, 65 calories per gram as the curve approaches the concentration pure iron, that is, as (N’/N) A 1. Just what is the real significance of polymerized molecules of (Fe&i)z existing in the melt and in solid solution, the writer is unable to say at present; neither is he interested in building up a mechanistic picture of such a compound. I n the final analysis, provided the determination of the liquidus and solidus curve is sufficiently accurate and the heat of fusion of the solvent metal is known, the constitution of the solute in solution is revealed with some certainty by the thermodynamic laws relating to tbe depression of the freezing point. There are, of course, other sources of evidence of the reality of the existence of molecular solutes in the liquid state (e.g., studies in magnetic susceptibility, resistance, specific volume, 5.9
5.8
$
5.7
5.6
5.8 0
0.01
0.02
0.03
044
log (N)/N))k
FIG.7. THELOG (N’/N).T-~CURVESPLOTTED ACCORDING TO EQUATION 3 Raman spectra, etc.), although the existence of the molecular solute in solid solution is much more difficult to prove. Given a saturated metallic solid solution in equilibrium with some excess solid solute in the form of an intermetallic ?ompound AB; the common conception is that AB is dissociated to A B upon dissolution in the solid solution. It is difficult to conceive, from strictly thermodynamic considerations, of the solute molecules magically dissociated in solution and yet in equilibrium with the solid solute (AB) whose dissociation pressure may be extremely small. I have already pointed out elsewhere (4)that if this were true, it should then be easy enough to construct a perpetual machine by simply lowering and elevating the temperature of a saturated solid solution. In order to ascertain if the degree of error in the thermal analysis can adequately account for the displacement of curve I1 in figure 7 from the
+
STUDY OF IRON-RICH IRON-SILICON ALLOYS
963
ideal position, backward calculations were made on the assumption that the solidus is correct, as it was determined by Haughton and Becker by the Heycock-Neville m e t h ~ d . ~ The calculated error in the location of the liquidus appears too large to be accounted for in this manner. The effect of silicon vapor on the reproducibility of a thermocouple is well-known and the accuracy of t,he thermal analysis of the primary solidification range may not be any better than &5"C. On this assumption, the liquidus and solidus curves drawn by Haughton and Becker have been redrawn as shown in figure 8, in which (Fe3Si)z is shown to have a definite melting point a t 125OoC,
11%
5
lo
15 20
:
Per cent Silicon
OF IRON-SILICONALLOYS (AFTER HAUGETON AND BECKER)
FIG. 8. THE PRIMARY SOLIDIFICATION RANQE
STABILITY OF SOLID SOLUTIONS
Some remarks regarding liquation (i.e., unmixing) and consequent segregation of the components in solid solution may not be amiss in this paper. Let us conceive of a metallic system, A and B, which forms a complete series of solid solutions and in which no compounds are formed in the melt. The free energy of the system is a t a minimum when A and B are distributed in such a manner that any unit portion (say a unit cell) has the same free energy content as any other unit portion, It is obvious that in a cubic system this condition is attained in the solid state only when the atomic fraction is a multiple of 1/8 when the solute atoms can be assigned a definite 7 The Heycock-Neville method involves quenching alloy specimens to successively higher temperatures and then examining the structure microscopically. The structure will be quite characteristic when the solidus temperature is reached.
964
CHU-PHAY YAP
position in the space lattice. This is the basis of Tammann’s conception of regular distribution as “limits of resistance,” as opposed to Vegard’s view of the atoms being statistically (irregularly) distributed. I n the liquid state where the atomic (and molecular) mobilities are much higher than in the solid state, a statistical distribution satisfies our conception of a homogeneous system, characterized by the lowest free energy; on the other hand, a solid solution may be expected to approach true homogeneity only as it approaches some form of regular distribution. When a solid solution is truly homogeneous, its free energy per mole (or gram-atom) is given by the equation
+
F = N ~ P ~N ~ =FRT(Nlln ~ al
+ N h I at)
(4)
where Fland p2 are the partial molal free energies of transfer of A and B (indicated for convenience by subscripts 1 and 2, respectively) from the pure state to a solid solution of activities al and a2,respectively. When the system obeys the laws of ideal solution, then al = N~ and az = N~ and their respective activities will vary linearly from 1to 0 as shown in figure 9. The activity-composition curves (1’) and (2’) indicate a negative deviation, hence a tendency towards compound formation. If the activity-composition curves were something like those shown in figure 10, all solid solutions between the composition of X and Y will have a tendency towards unmixing, whilst between A and X and between Y and B, a strong tendency towards compound formation exists ( 5 ) . The problem then arises as to which of these two opposing tendencies is the more dominant and under what conditions one is more likely to occur than the other. From strictly graphical analysis of the phase diagram, when the solidification range of the solid solutions is wide, we may reasonably anticipate the system to show a tendency to liquate.8 When the liquidus and solidus curves are very close together, then the solid solutions will melt over such a small temperature range as to behave as a unary substance, i.e., as a compound in this case. It should be noted, however, from phase-rule considerations, that as long as we have a solid solution, there will be a temperature range of melting, however small. The problem now arises as to whether or not a regular distribution is a compound. According to our strict interpretation of homogeneity (based on the elementary cell as a unit) a regular distribution merely represents an extreme form of an ideally homogeneous distribution in the solid state, but it is also self-evident that we are stretching the criterion of homogeneity
* This fact will become more evident when we recall that the phase diagram of two substances completely immiscible in each other in the solid and liquid states is given by two horizontal lines erected at their respective meltingpoints, extending from one component to the other; if the liquidus and solidus curves become spaced wider and wider apart, naturally they will approach, as a limit, these two horizontal lines.
STUDY O F IRON-RICH IRON-SILICON
ALLOYS
965
much further than is warranted even in the case of liquid solutions. It is thus quite conceivable that even if the unit of homogeneity were a thousandfold larger than an elementary cell, an aqueous solution might likewise appear to be inhomogeneous, especially if the solute molecules were quite large. Let us, therefore, seek elsewhere some other criterion of the nature of a regular distribution. I n the first place, it cannot be denied that some sort of chemical affinity is implicit in the tendency towards a regular distribution, because there is absolutely no reason on the basis of probability why the solute atoms can be made to distribute so regularly in the space
. A
Mote Fraction B
B
A
X
Y Mole Fraction B
B
FIG.9 FIQ.10 FIG. 9. ACTIVITY-COMPOSITION CURVES The linear activity-composition curves 1 and 2 indicate that the solid solutions are ideal from A to B. The negative deviations of the activity-composition curves 1’ and 2’ indicate a strong tendency to compound formation, although the compound formation is incomplete.
FIG.10. ACTIVITY-COMPOSITION CURVES The activity-composition curves indicate a tendency to compound formation between A-X and Y-B and a tendency t o liquation between X-Y.
lattice. If a regular lattice merely represents a special form of solid solution, whose free energy is at a minimum, then the perplexing question arises as to why once the regular distribution is obtained, it can be destroyed again by merely heat,ing up to a certain temperature and cooling down rapidly. On the assumption that a regular distribution is a compound, the critical temperature then corresponds to a melting phenomenon in tjhe solid state. When the solvent and solute atoms have some affinity for each other to form compounds, their size and shape must undergo some alteration as a result of 6he alteration in their electronic configurations (e.g., as due to
966
CHU-PHAY YAP
sharing of electrons) and consequently their crystallographic habits will likewise be modified. The larger the affinity, the more marked will the alteration be, so that the compound may actually crystallize in an entirely different system, although it should be noted that often it is simply a matter of changing the crystallographic axes of referen~e.~ It is certainly curious that a solid solution, in its tendency to liquate or unmix and to form a regular structure, behaves like a dispersed system. A system in which all the dispersed particles are of the same size and therefore, possessing the same surface energy per particle, may theoretically be expected to be rather stable and should show little or no tendency towards aggregation; it is only owing to the difference in the surface energy of the dispersed particles of varying size that we have a tendency towards aggregation,1° which may eventually lead to two equally stable states, vie., (1) a state in which the dispersed particles finally aggregate into a single large particle and (2) a state in which all particles again assume the same, though larger, particle-size. The former state is equivalent to the liquation tendency in solid solutions described above, while the latter is similar to the tendency to form a regular distribution. The writer hopes to work out these theoretical relationships in more detail in the future. SUMMARY
1. On the basis of the results obtained in the study of some iron-silicon alloys of high purity, by means of the thermoelectric method, electrode potential measurements and x-ray crystal analysis, it is concluded that FeaSi (6)is a compound and not merely a distinguished point in a series of solid solutions. The existence of Fe3Si2(7) and FeSi (E) is also indicated by the electrode potential measurements, without direct evidence, however, of their actual chemical composition. 2. By the thermodynamic method of studying the depression in the freezing point, it is shown that the actual composition of 6 is (FeaSi)zor Fe6Siz. 3. In the hope of helping to clarify some of our conceptions regarding the stability of solid solutions, the tendency to liquation (i.e., unmixing) and formation of regular distribution, has been discussed at some length from To illustrate: If A and B crystallize in the face-centered cubic system, but the regular distribution crystallizes in the body-centered tetragonal system with, say, c/a = 1.5. Then if we choose different crystallographic axes of reference for the facecentered cube and treat A and B as crystallizing in the body-centered tetragonal system with c/a = 1.414, the crystallographic differences become much less and more understandable. 10 This is because the system is not in equilibrium, because although the usual parameters of the free energy (pressure, temperature, and composition) are defined, the change in the free energy with respect to the surface ( d F / d u ) p , ~ ,has ~ not been determined. Hence, the system will possess an additional degree of freedom.
STUDY OF IRON-RICH IRON-SILICON ALLOYS
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the thermodynamic point of view. Reasons why a solid solution with a regular distribution should be treated as a compound, have been advanced. The facilities for carrying out this investigation in the Department of Chemist,ry, Washington Square College of New York University, were kindly provided by Professor Ehret (who read the proof in the absence of the author), and to him and to Professor King the writer desires to express his cordial thanks for t8heirfriendly interest and suggestions during the progress of the work. Special mention should be made of the diligent assistance of Messrs. Diller and Abramson-the former for making the thermoelectric study, and the latter for taking numerous e1ect)rode potential readings. REFERENCES (1) HAUQHTON, J. L., AND BECKER, M.: J. Iron Steel Inst. London 121, 315 (1930). STOUGHTON, B., AND GREINER, E. S.: Trans. Am. Inst. Mining Met. Engrs., Iron and Steel Division, p. 155 (1930). CORSON, M. G. : Trans. Am. Inst. Mining Met. Engrs., Iron and Steel Division, p. 249 (1928). MURAKAYI, T.: Science Repts. TBhoku Imp. C'niv. 10, 79 (1921); 16, 475 (1927). PHRAQMEN, G.: J. Iron Steel Inst. London 114, 397 (1926). BAMBERGER, M., EINERL, O., AND NUSSBAUM, J. : Stahl u. Eisen 44, 141 (1925). KURNAKOFF, N., AND URAZOFF, G.: Z. anorg. chem. 123, 89 (1922). SANFOURCHE, M. A.: Rev. m6t. 16, 217 (1919). GONTERMANN, W. : Z. anorg. Chem. 68,384 (1908). GUERTLER, W., AND TAMMANN, G.: Z. anorg. Chem. 47, 163 (1908). (2) YAP,C. P. : Trans. Faraday Soc. 27,777 (1931). (3) HILDEBRAND, J. H. : Solubility. Chemical Catalog Co., New York (1924). (4) Consult for example, a recent paper on the system: NaC1-AgC1 by A. WACHTER: J. Am. Chem. SOC.64, 919 (1932).
